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ENGINEERING (1248 journals)                  1 2 3 4 5 6 7 | Last

Showing 1 - 200 of 1205 Journals sorted alphabetically
3 Biotech     Open Access   (Followers: 8)
3D Research     Hybrid Journal   (Followers: 20)
AAPG Bulletin     Hybrid Journal   (Followers: 8)
AASRI Procedia     Open Access   (Followers: 14)
Abstract and Applied Analysis     Open Access   (Followers: 3)
Aceh International Journal of Science and Technology     Open Access   (Followers: 2)
ACS Nano     Full-text available via subscription   (Followers: 277)
Acta Geotechnica     Hybrid Journal   (Followers: 7)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 7)
Acta Polytechnica : Journal of Advanced Engineering     Open Access   (Followers: 3)
Acta Scientiarum. Technology     Open Access   (Followers: 3)
Acta Universitatis Cibiniensis. Technical Series     Open Access  
Active and Passive Electronic Components     Open Access   (Followers: 7)
Adaptive Behavior     Hybrid Journal   (Followers: 11)
Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi     Open Access  
Adsorption     Hybrid Journal   (Followers: 4)
Advanced Engineering Forum     Full-text available via subscription   (Followers: 7)
Advanced Science     Open Access   (Followers: 5)
Advanced Science Focus     Free   (Followers: 5)
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advanced Science, Engineering and Medicine     Partially Free   (Followers: 7)
Advanced Synthesis & Catalysis     Hybrid Journal   (Followers: 18)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Engineering Software     Hybrid Journal   (Followers: 27)
Advances in Fuel Cells     Full-text available via subscription   (Followers: 15)
Advances in Fuzzy Systems     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Heat Transfer     Full-text available via subscription   (Followers: 21)
Advances in Human Factors/Ergonomics     Full-text available via subscription   (Followers: 22)
Advances in Magnetic and Optical Resonance     Full-text available via subscription   (Followers: 9)
Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (Followers: 29)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in OptoElectronics     Open Access   (Followers: 5)
Advances in Physics Theories and Applications     Open Access   (Followers: 13)
Advances in Polymer Science     Hybrid Journal   (Followers: 43)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Remote Sensing     Open Access   (Followers: 44)
Advances in Science and Research (ASR)     Open Access   (Followers: 5)
Aerobiologia     Hybrid Journal   (Followers: 3)
African Journal of Science, Technology, Innovation and Development     Hybrid Journal   (Followers: 6)
AIChE Journal     Hybrid Journal   (Followers: 35)
Ain Shams Engineering Journal     Open Access   (Followers: 5)
Akademik Platform Mühendislik ve Fen Bilimleri Dergisi     Open Access   (Followers: 1)
Alexandria Engineering Journal     Open Access   (Followers: 1)
AMB Express     Open Access   (Followers: 1)
American Journal of Applied Sciences     Open Access   (Followers: 26)
American Journal of Engineering and Applied Sciences     Open Access   (Followers: 10)
American Journal of Engineering Education     Open Access   (Followers: 9)
American Journal of Environmental Engineering     Open Access   (Followers: 16)
American Journal of Industrial and Business Management     Open Access   (Followers: 23)
Analele Universitatii Ovidius Constanta - Seria Chimie     Open Access  
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of Regional Science     Hybrid Journal   (Followers: 7)
Annals of Science     Hybrid Journal   (Followers: 7)
Antarctic Science     Hybrid Journal   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applicable Analysis: An International Journal     Hybrid Journal   (Followers: 1)
Applied Catalysis A: General     Hybrid Journal   (Followers: 6)
Applied Catalysis B: Environmental     Hybrid Journal   (Followers: 18)
Applied Clay Science     Hybrid Journal   (Followers: 6)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 4)
Applied Nanoscience     Open Access   (Followers: 8)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Physics Research     Open Access   (Followers: 5)
Applied Sciences     Open Access   (Followers: 3)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arabian Journal for Science and Engineering     Hybrid Journal   (Followers: 5)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Archives of Foundry Engineering     Open Access  
Archives of Thermodynamics     Open Access   (Followers: 8)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
ASEE Prism     Full-text available via subscription   (Followers: 3)
Asia-Pacific Journal of Science and Technology     Open Access  
Asian Engineering Review     Open Access  
Asian Journal of Applied Science and Engineering     Open Access   (Followers: 1)
Asian Journal of Applied Sciences     Open Access   (Followers: 2)
Asian Journal of Biotechnology     Open Access   (Followers: 8)
Asian Journal of Control     Hybrid Journal  
Asian Journal of Current Engineering & Maths     Open Access  
Asian Journal of Technology Innovation     Hybrid Journal   (Followers: 8)
Assembly Automation     Hybrid Journal   (Followers: 2)
at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
ATZagenda     Hybrid Journal  
ATZextra worldwide     Hybrid Journal  
Australasian Physical & Engineering Sciences in Medicine     Hybrid Journal   (Followers: 1)
Australian Journal of Multi-Disciplinary Engineering     Full-text available via subscription   (Followers: 2)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 9)
Avances en Ciencias e Ingeniería     Open Access  
Balkan Region Conference on Engineering and Business Education     Open Access   (Followers: 1)
Bangladesh Journal of Scientific and Industrial Research     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
Batteries     Open Access   (Followers: 6)
Bautechnik     Hybrid Journal   (Followers: 1)
Bell Labs Technical Journal     Hybrid Journal   (Followers: 26)
Beni-Suef University Journal of Basic and Applied Sciences     Open Access   (Followers: 4)
BER : Manufacturing Survey : Full Survey     Full-text available via subscription   (Followers: 1)
BER : Motor Trade Survey     Full-text available via subscription  
BER : Retail Sector Survey     Full-text available via subscription   (Followers: 1)
BER : Retail Survey : Full Survey     Full-text available via subscription   (Followers: 1)
BER : Survey of Business Conditions in Manufacturing : An Executive Summary     Full-text available via subscription   (Followers: 2)
BER : Survey of Business Conditions in Retail : An Executive Summary     Full-text available via subscription   (Followers: 3)
Beyond : Undergraduate Research Journal     Open Access  
Bhakti Persada : Jurnal Aplikasi IPTEKS     Open Access  
Bharatiya Vaigyanik evam Audyogik Anusandhan Patrika (BVAAP)     Open Access   (Followers: 1)
Biofuels Engineering     Open Access   (Followers: 1)
Biointerphases     Open Access   (Followers: 1)
Biomaterials Science     Full-text available via subscription   (Followers: 10)
Biomedical Engineering     Hybrid Journal   (Followers: 15)
Biomedical Engineering and Computational Biology     Open Access   (Followers: 13)
Biomedical Engineering Letters     Hybrid Journal   (Followers: 5)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 21)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 37)
Biomedical Engineering: Applications, Basis and Communications     Hybrid Journal   (Followers: 5)
Biomedical Microdevices     Hybrid Journal   (Followers: 9)
Biomedical Science and Engineering     Open Access   (Followers: 4)
Biomedizinische Technik - Biomedical Engineering     Hybrid Journal  
Biomicrofluidics     Open Access   (Followers: 4)
BioNanoMaterials     Hybrid Journal   (Followers: 2)
Biotechnology Progress     Hybrid Journal   (Followers: 39)
Boletin Cientifico Tecnico INIMET     Open Access  
Botswana Journal of Technology     Full-text available via subscription   (Followers: 1)
Boundary Value Problems     Open Access   (Followers: 1)
Brazilian Journal of Science and Technology     Open Access   (Followers: 2)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 12)
Bulletin of Canadian Petroleum Geology     Full-text available via subscription   (Followers: 13)
Bulletin of Engineering Geology and the Environment     Hybrid Journal   (Followers: 14)
Bulletin of the Crimean Astrophysical Observatory     Hybrid Journal  
Cahiers, Droit, Sciences et Technologies     Open Access  
Calphad     Hybrid Journal  
Canadian Geotechnical Journal     Hybrid Journal   (Followers: 31)
Canadian Journal of Remote Sensing     Full-text available via subscription   (Followers: 42)
Case Studies in Engineering Failure Analysis     Open Access   (Followers: 6)
Case Studies in Thermal Engineering     Open Access   (Followers: 5)
Catalysis Communications     Hybrid Journal   (Followers: 6)
Catalysis Letters     Hybrid Journal   (Followers: 2)
Catalysis Reviews: Science and Engineering     Hybrid Journal   (Followers: 7)
Catalysis Science and Technology     Free   (Followers: 8)
Catalysis Surveys from Asia     Hybrid Journal   (Followers: 3)
Catalysis Today     Hybrid Journal   (Followers: 7)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
Cellular and Molecular Neurobiology     Hybrid Journal   (Followers: 3)
Central European Journal of Engineering     Hybrid Journal  
CFD Letters     Open Access   (Followers: 6)
Chaos : An Interdisciplinary Journal of Nonlinear Science     Hybrid Journal   (Followers: 2)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Engineering     Open Access   (Followers: 2)
Chinese Science Bulletin     Open Access   (Followers: 1)
Ciencia e Ingenieria Neogranadina     Open Access  
Ciencia en su PC     Open Access   (Followers: 1)
Ciencias Holguin     Open Access   (Followers: 3)
CienciaUAT     Open Access   (Followers: 1)
Cientifica     Open Access  
CIRP Annals - Manufacturing Technology     Full-text available via subscription   (Followers: 11)
CIRP Journal of Manufacturing Science and Technology     Full-text available via subscription   (Followers: 13)
City, Culture and Society     Hybrid Journal   (Followers: 21)
Clay Minerals     Full-text available via subscription   (Followers: 10)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Clinical Science     Full-text available via subscription   (Followers: 9)
Coal Science and Technology     Full-text available via subscription   (Followers: 3)
Coastal Engineering     Hybrid Journal   (Followers: 11)
Coastal Engineering Journal     Hybrid Journal   (Followers: 6)
Coatings     Open Access   (Followers: 4)
Cogent Engineering     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Color Research & Application     Hybrid Journal   (Followers: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Combustion, Explosion, and Shock Waves     Hybrid Journal   (Followers: 13)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Numerical Methods in Engineering     Hybrid Journal   (Followers: 2)
Components, Packaging and Manufacturing Technology, IEEE Transactions on     Hybrid Journal   (Followers: 28)
Composite Interfaces     Hybrid Journal   (Followers: 7)
Composite Structures     Hybrid Journal   (Followers: 277)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 213)
Composites Part B : Engineering     Hybrid Journal   (Followers: 248)
Composites Science and Technology     Hybrid Journal   (Followers: 188)
Comptes Rendus Mécanique     Full-text available via subscription   (Followers: 2)
Computation     Open Access  
Computational Geosciences     Hybrid Journal   (Followers: 15)
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computer Applications in Engineering Education     Hybrid Journal   (Followers: 8)
Computer Science and Engineering     Open Access   (Followers: 19)
Computers & Geosciences     Hybrid Journal   (Followers: 31)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Computers and Electronics in Agriculture     Hybrid Journal   (Followers: 5)
Computers and Geotechnics     Hybrid Journal   (Followers: 11)
Computing and Visualization in Science     Hybrid Journal   (Followers: 6)
Computing in Science & Engineering     Full-text available via subscription   (Followers: 33)
Conciencia Tecnologica     Open Access  
Concurrent Engineering     Hybrid Journal   (Followers: 3)
Continuum Mechanics and Thermodynamics     Hybrid Journal   (Followers: 8)
Control and Dynamic Systems     Full-text available via subscription   (Followers: 9)
Control Engineering Practice     Hybrid Journal   (Followers: 43)

        1 2 3 4 5 6 7 | Last

Journal Cover Computational Optimization and Applications
  [SJR: 1.481]   [H-I: 54]   [7 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1573-2894 - ISSN (Online) 0926-6003
   Published by Springer-Verlag Homepage  [2350 journals]
  • Parallel cyclic reduction strategies for linear systems that arise in
           dynamic optimization problems
    • Authors: Bethany L. Nicholson; Wei Wan; Shivakumar Kameswaran; Lorenz T. Biegler
      Pages: 321 - 350
      Abstract: Dynamic optimization problems are constrained by differential and algebraic equations and are found everywhere in science and engineering. A well-established method to solve these types of problems is direct transcription, where the differential equations are replaced with discretized approximations based on finite-difference or Runge–Kutta schemes. However, for problems with thousands of state variables and discretization points, direct transcription may result in nonlinear optimization problems which are too large for general-purpose optimization solvers to handle. Also, when an interior-point solver is applied, the dominant computational cost is solving the linear systems resulting from the Newton step. For large-scale nonlinear programming problems, these linear systems may become prohibitively expensive to solve. Furthermore, the systems also become too large to formulate and store in memory of a standard computer. On the other hand, direct transcription can exploit sparsity and structure of the linear systems in order to overcome these challenges. In this paper we investigate and compare two parallel linear decomposition algorithms, Cyclic Reduction (CR) and Schur complement decomposition, which take advantage of structure and sparsity. We describe the numerical conditioning of the CR algorithm when applied to the linear systems arising from dynamic optimization problems, and then compare CR with Schur complement decomposition on a number of test problems. Finally, we propose conditions under which each should be used, and describe future research directions.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0001-7
      Issue No: Vol. 70, No. 2 (2018)
  • A nonconvex formulation for low rank subspace clustering: algorithms and
           convergence analysis
    • Authors: Hao Jiang; Daniel P. Robinson; René Vidal; Chong You
      Pages: 395 - 418
      Abstract: We consider the problem of subspace clustering with data that is potentially corrupted by both dense noise and sparse gross errors. In particular, we study a recently proposed low rank subspace clustering approach based on a nonconvex modeling formulation. This formulation includes a nonconvex spectral function in the objective function that makes the optimization task challenging, e.g., it is unknown whether the alternating direction method of multipliers (ADMM) framework proposed to solve the nonconvex model formulation is provably convergent. In this paper, we establish that the spectral function is differentiable and give a formula for computing the derivative. Moreover, we show that the derivative of the spectral function is Lipschitz continuous and provide an explicit value for the Lipschitz constant. These facts are then used to provide a lower bound for how the penalty parameter in the ADMM method should be chosen. As long as the penalty parameter is chosen according to this bound, we show that the ADMM algorithm computes iterates that have a limit point satisfying first-order optimality conditions. We also present a second strategy for solving the nonconvex problem that is based on proximal gradient calculations. The convergence and performance of the algorithms is verified through experiments on real data from face and digit clustering and motion segmentation.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0002-6
      Issue No: Vol. 70, No. 2 (2018)
  • Completely positive tensor recovery with minimal nuclear value
    • Authors: Anwa Zhou; Jinyan Fan
      Pages: 419 - 441
      Abstract: In this paper, we introduce the CP-nuclear value of a completely positive (CP) tensor and study its properties. A semidefinite relaxation algorithm is proposed for solving the minimal CP-nuclear-value tensor recovery. If a partial tensor is CP-recoverable, the algorithm can give a CP tensor recovery with the minimal CP-nuclear value, as well as a CP-nuclear decomposition of the recovered CP tensor. If it is not CP-recoverable, the algorithm can always give a certificate for that, when it is regular. Some numerical experiments are also presented.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0003-5
      Issue No: Vol. 70, No. 2 (2018)
  • Chance-constrained economic dispatch with renewable energy and storage
    • Authors: Jianqiang Cheng; Richard Li-Yang Chen; Habib N. Najm; Ali Pinar; Cosmin Safta; Jean-Paul Watson
      Pages: 479 - 502
      Abstract: Increasing penetration levels of renewables have transformed how power systems are operated. High levels of uncertainty in production make it increasingly difficulty to guarantee operational feasibility; instead, constraints may only be satisfied with high probability. We present a chance-constrained economic dispatch model that efficiently integrates energy storage and high renewable penetration to satisfy renewable portfolio requirements. Specifically, we require that wind energy contribute at least a prespecified proportion of the total demand and that the scheduled wind energy is deliverable with high probability. We develop an approximate partial sample average approximation (PSAA) framework to enable efficient solution of large-scale chance-constrained economic dispatch problems. Computational experiments on the IEEE-24 bus system show that the proposed PSAA approach is more accurate, closer to the prescribed satisfaction tolerance, and approximately 100 times faster than standard sample average approximation. Finally, the improved efficiency of our PSAA approach enables solution of a larger WECC-240 test system in minutes.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0006-2
      Issue No: Vol. 70, No. 2 (2018)
  • Efficiently solving total least squares with Tikhonov identical
    • Authors: Meijia Yang; Yong Xia; Jiulin Wang; Jiming Peng
      Pages: 571 - 592
      Abstract: The Tikhonov identical regularized total least squares (TI) is to deal with the ill-conditioned system of linear equations where the data are contaminated by noise. A standard approach for (TI) is to reformulate it as a problem of finding a zero point of some decreasing concave non-smooth univariate function such that the classical bisection search and Dinkelbach’s method can be applied. In this paper, by exploring the hidden convexity of (TI), we reformulate it as a new problem of finding a zero point of a strictly decreasing, smooth and concave univariate function. This allows us to apply the classical Newton’s method to the reformulated problem, which converges globally to the unique root with an asymptotic quadratic convergence rate. Moreover, in every iteration of Newton’s method, no optimization subproblem such as the extended trust-region subproblem is needed to evaluate the new univariate function value as it has an explicit expression. Promising numerical results based on the new algorithm are reported.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0004-4
      Issue No: Vol. 70, No. 2 (2018)
  • A linear-time algorithm to compute the conjugate of convex piecewise
           linear-quadratic bivariate functions
    • Authors: Tasnuva Haque; Yves Lucet
      Pages: 593 - 613
      Abstract: We propose the first algorithm to compute the conjugate of a bivariate Piecewise Linear-Quadratic (PLQ) function in optimal linear worst-case time complexity. The key step is to use a planar graph, called the entity graph, not only to represent the entities (vertex, edge, or face) of the domain of a PLQ function but most importantly to record adjacent entities. We traverse the graph using breadth-first search to compute the conjugate of each entity using graph-matrix calculus, and use the adjacency information to create the output data structure in linear time.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0007-1
      Issue No: Vol. 70, No. 2 (2018)
  • A second-order optimality condition with first- and second-order
           complementarity associated with global convergence of algorithms
    • Authors: Gabriel Haeser
      Pages: 615 - 639
      Abstract: We develop a new notion of second-order complementarity with respect to the tangent subspace related to second-order necessary optimality conditions by the introduction of so-called tangent multipliers. We prove that around a local minimizer, a second-order stationarity residual can be driven to zero while controlling the growth of Lagrange multipliers and tangent multipliers, which gives a new second-order optimality condition without constraint qualifications stronger than previous ones associated with global convergence of algorithms. We prove that second-order variants of augmented Lagrangian (under an additional smoothness assumption based on the Lojasiewicz inequality) and interior point methods generate sequences satisfying our optimality condition. We present also a companion minimal constraint qualification, weaker than the ones known for second-order methods, that ensures usual global convergence results to a classical second-order stationary point. Finally, our optimality condition naturally suggests a definition of second-order stationarity suitable for the computation of iteration complexity bounds and for the definition of stopping criteria.
      PubDate: 2018-06-01
      DOI: 10.1007/s10589-018-0005-3
      Issue No: Vol. 70, No. 2 (2018)
  • A copositive approach for two-stage adjustable robust optimization with
           uncertain right-hand sides
    • Authors: Guanglin Xu; Samuel Burer
      Pages: 33 - 59
      Abstract: We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which in turn leads to a class of tractable, semidefinite-based approximations that are at least as strong as the affine policy. We investigate several examples from the literature demonstrating that our tractable approximations significantly improve the affine policy. In particular, our approach solves exactly in polynomial time a class of instances of increasing size for which the affine policy admits an arbitrarily large gap.
      PubDate: 2018-05-01
      DOI: 10.1007/s10589-017-9974-x
      Issue No: Vol. 70, No. 1 (2018)
  • Accelerated primal–dual proximal block coordinate updating methods for
           constrained convex optimization
    • Authors: Yangyang Xu; Shuzhong Zhang
      Pages: 91 - 128
      Abstract: Block coordinate update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks. They are also easily parallelized and thus have been particularly popular for solving problems involving large-scale dataset and/or variables. In this paper, we propose a primal–dual BCU method for solving linearly constrained convex program with multi-block variables. The method is an accelerated version of a primal–dual algorithm proposed by the authors, which applies randomization in selecting block variables to update and establishes an O(1 / t) convergence rate under convexity assumption. We show that the rate can be accelerated to \(O(1/t^2)\) if the objective is strongly convex. In addition, if one block variable is independent of the others in the objective, we then show that the algorithm can be modified to achieve a linear rate of convergence. The numerical experiments show that the accelerated method performs stably with a single set of parameters while the original method needs to tune the parameters for different datasets in order to achieve a comparable level of performance.
      PubDate: 2018-05-01
      DOI: 10.1007/s10589-017-9972-z
      Issue No: Vol. 70, No. 1 (2018)
  • Two smooth support vector machines for $$\varepsilon $$ ε -insensitive
    • Authors: Weizhe Gu; Wei-Po Chen; Chun-Hsu Ko; Yuh-Jye Lee; Jein-Shan Chen
      Pages: 171 - 199
      Abstract: In this paper, we propose two new smooth support vector machines for \(\varepsilon \) -insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to \(\varepsilon \) -support vector regression ( \(\varepsilon \) -SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.
      PubDate: 2018-05-01
      DOI: 10.1007/s10589-017-9975-9
      Issue No: Vol. 70, No. 1 (2018)
  • MIP-based instantaneous control of mixed-integer PDE-constrained gas
           transport problems
    • Authors: Martin Gugat; Günter Leugering; Alexander Martin; Martin Schmidt; Mathias Sirvent; David Wintergerst
      Pages: 267 - 294
      Abstract: We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.
      PubDate: 2018-05-01
      DOI: 10.1007/s10589-017-9970-1
      Issue No: Vol. 70, No. 1 (2018)
  • Tikhonov regularization of control-constrained optimal control problems
    • Authors: Nikolaus von Daniels
      Pages: 295 - 320
      Abstract: We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang–bang solutions, we introduce another assumption to obtain the same convergence rates. This new condition turns out to be useful in the derivation of error estimates for the discretized problem. The necessity of the just mentioned assumptions to obtain certain convergence rates is analyzed. Finally, a numerical example confirms the analytical findings.
      PubDate: 2018-05-01
      DOI: 10.1007/s10589-017-9976-8
      Issue No: Vol. 70, No. 1 (2018)
  • A flexible coordinate descent method
    • Authors: Kimon Fountoulakis; Rachael Tappenden
      Abstract: We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of FCD, a block of coordinates is sampled randomly, a quadratic model is formed about that block and the model is minimized approximately/inexactly to determine the search direction. An inexpensive line search is then employed to ensure a monotonic decrease in the objective function and acceptance of large step sizes. We present several high probability iteration complexity results to show that convergence of FCD is guaranteed theoretically. Finally, we present numerical results on large-scale problems to demonstrate the practical performance of the method.
      PubDate: 2018-02-24
      DOI: 10.1007/s10589-018-9984-3
  • Convergence of a Scholtes-type regularization method for
           cardinality-constrained optimization problems with an application in
           sparse robust portfolio optimization
    • Authors: Martin Branda; Max Bucher; Michal Červinka; Alexandra Schwartz
      Abstract: We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming problem, which is thus still difficult to solve. Therefore, we apply a Scholtes-type regularization method to obtain a sequence of easier to solve problems and investigate the convergence of the obtained KKT points. We show that such a sequence converges to an S-stationary point, which corresponds to a local minimizer of the original problem under the assumption of convexity. Additionally, we consider portfolio optimization problems where we minimize a risk measure under a cardinality constraint on the portfolio. Various risk measures are considered, in particular Value-at-Risk and Conditional Value-at-Risk under normal distribution of returns and their robust counterparts under moment conditions. For these investment problems formulated as nonlinear programming problems with cardinality constraints we perform a numerical study on a large number of simulated instances taken from the literature and illuminate the computational performance of the Scholtes-type regularization method in comparison to other considered solution approaches: a mixed-integer solver, a direct continuous reformulation solver and the Kanzow–Schwartz regularization method, which has already been applied to Markowitz portfolio problems.
      PubDate: 2018-02-21
      DOI: 10.1007/s10589-018-9985-2
  • A primal-dual homotopy algorithm for $$\ell _{1}$$ ℓ 1 -minimization
           with $$\ell _{\infty }$$ ℓ ∞ -constraints
    • Authors: Christoph Brauer; Dirk A. Lorenz; Andreas M. Tillmann
      Abstract: In this paper we propose a primal-dual homotopy method for \(\ell _1\) -minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem and a respective piecewise constant path for the dual problem. We show that by solving a small linear program, one can jump to the next primal break point and then, solving another small linear program, a new optimal dual solution is calculated which enables the next such jump in the subsequent iteration. Using a theorem of the alternative, we show that the method never gets stuck and indeed calculates the whole path in a finite number of steps. Numerical experiments demonstrate the effectiveness of our algorithm. In many cases, our method significantly outperforms commercial LP solvers; this is possible since our approach employs a sequence of considerably simpler auxiliary linear programs that can be solved efficiently with specialized active-set strategies.
      PubDate: 2018-02-15
      DOI: 10.1007/s10589-018-9983-4
  • Adaptive optimal control of Signorini’s problem
    • Authors: Andreas Rademacher; Korinna Rosin
      Abstract: In this article, we present a-posteriori error estimations in context of optimal control of contact problems; in particular of Signorini’s problem. Due to the contact side-condition, the solution operator of the underlying variational inequality is not differentiable, yet we want to apply Newton’s method. Therefore, the non-smooth problem is regularized by penalization and afterwards discretized by finite elements. We derive optimality systems for the regularized formulation in the continuous as well as in the discrete case. This is done explicitly for Signorini’s contact problem, which covers linear elasticity and linearized surface contact conditions. The latter creates the need for treating trace-operations carefully, especially in contrast to obstacle contact conditions, which exert in the domain. Based on the dual weighted residual method and these optimality systems, we deduce error representations for the regularization, discretization and numerical errors. Those representations are further developed into error estimators. The resulting error estimator for regularization error is defined only in the contact area. Therefore its computational cost is especially low for Signorini’s contact problem. Finally, we utilize the estimators in an adaptive refinement strategy balancing regularization and discretization errors. Numerical results substantiate the theoretical findings. We present different examples concerning Signorini’s problem in two and three dimensions.
      PubDate: 2018-01-31
      DOI: 10.1007/s10589-018-9982-5
  • On the convergence of the gradient projection method for convex optimal
           control problems with bang–bang solutions
    • Authors: J. Preininger; P. T. Vuong
      Abstract: We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.
      PubDate: 2018-01-29
      DOI: 10.1007/s10589-018-9981-6
  • Improved approximation rates for a parabolic control problem with an
           objective promoting directional sparsity
    • Authors: Eduardo Casas; Mariano Mateos; Arnd Rösch
      Abstract: We discretize a directionally sparse parabolic control problem governed by a linear equation by means of control approximations that are piecewise constant in time and continuous piecewise linear in space. By discretizing the objective functional with the help of appropriate numerical quadrature formulas, we are able to show that the discrete optimal solution exhibits a directional sparse pattern alike the one enjoyed by the continuous solution. Error estimates are obtained and a comparison with the cases of having piecewise approximations of the control or a semilinear state equation are discussed. Numerical experiments that illustrate the theoretical results are included.
      PubDate: 2018-01-27
      DOI: 10.1007/s10589-018-9979-0
  • Time-optimal velocity planning by a bound-tightening technique
    • Authors: Federico Cabassi; Luca Consolini; Marco Locatelli
      Abstract: Range reduction techniques often considerably enhance the performance of algorithmic approaches for the solution of nonconvex problems. In this paper we propose a range reduction technique for a class of optimization problems with some special structured constraints. The procedure explores and updates the values associated to the nodes of a suitably defined graph. Convergence of the procedure and some efficiency issues, in particular related to the order into which the nodes of the graph are explored. The proposed technique is applied to solve problems arising from a relevant practical application, namely velocity planning along a given trajectory. The computational experiments show the efficiency of the procedure and its ability of returning solutions within times much lower than those of nonlinear solvers and compatible with real-time applications.
      PubDate: 2018-01-11
      DOI: 10.1007/s10589-017-9978-6
  • Iterative reweighted methods for $$\ell _1-\ell _p$$ ℓ 1 - ℓ p
    • Authors: Xianchao Xiu; Lingchen Kong; Yan Li; Houduo Qi
      Abstract: In this paper, we focus on the \(\ell _1-\ell _p\) minimization problem with \(0<p<1\) , which is challenging due to the \(\ell _p\) norm being non-Lipschizian. In theory, we derive computable lower bounds for nonzero entries of the generalized first-order stationary points of \(\ell _1-\ell _p\) minimization, and hence of its local minimizers. In algorithms, based on three locally Lipschitz continuous \(\epsilon \) -approximation to \(\ell _p\) norm, we design several iterative reweighted \(\ell _1\) and \(\ell _2\) methods to solve those approximation problems. Furthermore, we show that any accumulation point of the sequence generated by these methods is a generalized first-order stationary point of \(\ell _1-\ell _p\) minimization. This result, in particular, applies to the iterative reweighted \(\ell _1\) methods based on the new Lipschitz continuous \(\epsilon \) -approximation introduced by Lu (Math Program 147(1–2):277–307, 2014), provided that the approximation parameter \(\epsilon \) is below a threshold value. Numerical results are also reported to demonstrate the efficiency of the proposed methods.
      PubDate: 2018-01-05
      DOI: 10.1007/s10589-017-9977-7
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