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  Subjects -> ENGINEERING (Total: 2270 journals)
    - CHEMICAL ENGINEERING (191 journals)
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    - ENGINEERING (1199 journals)
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ENGINEERING (1199 journals)                  1 2 3 4 5 6 | Last

Showing 1 - 200 of 1205 Journals sorted alphabetically
3 Biotech     Open Access   (Followers: 7)
3D Research     Hybrid Journal   (Followers: 19)
AAPG Bulletin     Full-text available via subscription   (Followers: 5)
AASRI Procedia     Open Access   (Followers: 15)
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: 217)
Acta Geotechnica     Hybrid Journal   (Followers: 6)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 5)
Acta Polytechnica : Journal of Advanced Engineering     Open Access   (Followers: 2)
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: 10)
Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi     Open Access  
Adsorption     Hybrid Journal   (Followers: 4)
Advanced Engineering Forum     Full-text available via subscription   (Followers: 4)
Advanced Science     Open Access   (Followers: 4)
Advanced Science Focus     Free   (Followers: 3)
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
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Advanced Synthesis & Catalysis     Hybrid Journal   (Followers: 17)
Advances in Artificial Neural Systems     Open Access   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
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Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Engineering Software     Hybrid Journal   (Followers: 25)
Advances in Fuel Cells     Full-text available via subscription   (Followers: 14)
Advances in Fuzzy Systems     Open Access   (Followers: 5)
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Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (Followers: 28)
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Advances in OptoElectronics     Open Access   (Followers: 5)
Advances in Physics Theories and Applications     Open Access   (Followers: 12)
Advances in Polymer Science     Hybrid Journal   (Followers: 40)
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Advances in Remote Sensing     Open Access   (Followers: 35)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aerobiologia     Hybrid Journal   (Followers: 1)
African Journal of Science, Technology, Innovation and Development     Hybrid Journal   (Followers: 4)
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Ain Shams Engineering Journal     Open Access   (Followers: 5)
Akademik Platform Mühendislik ve Fen Bilimleri Dergisi     Open Access  
Alexandria Engineering Journal     Open Access   (Followers: 1)
AMB Express     Open Access   (Followers: 1)
American Journal of Applied Sciences     Open Access   (Followers: 27)
American Journal of Engineering and Applied Sciences     Open Access   (Followers: 11)
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: 3)
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)
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: 8)
Applied Clay Science     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 3)
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Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Physics Research     Open Access   (Followers: 3)
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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: 4)
Archives of Foundry Engineering     Open Access  
Archives of Thermodynamics     Open Access   (Followers: 7)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
ASEE Prism     Full-text available via subscription   (Followers: 2)
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: 7)
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: 7)
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: 3)
Batteries     Open Access   (Followers: 3)
Bautechnik     Hybrid Journal   (Followers: 1)
Bell Labs Technical Journal     Hybrid Journal   (Followers: 23)
Beni-Suef University Journal of Basic and Applied Sciences     Open Access   (Followers: 3)
BER : Manufacturing Survey : Full Survey     Full-text available via subscription   (Followers: 2)
BER : Motor Trade Survey     Full-text available via subscription   (Followers: 1)
BER : Retail Sector Survey     Full-text available via subscription   (Followers: 2)
BER : Retail Survey : Full Survey     Full-text available via subscription   (Followers: 2)
BER : Survey of Business Conditions in Manufacturing : An Executive Summary     Full-text available via subscription   (Followers: 3)
BER : Survey of Business Conditions in Retail : An Executive Summary     Full-text available via subscription   (Followers: 3)
Bharatiya Vaigyanik evam Audyogik Anusandhan Patrika (BVAAP)     Open Access   (Followers: 1)
Biofuels Engineering     Open Access  
Biointerphases     Open Access   (Followers: 1)
Biomaterials Science     Full-text available via subscription   (Followers: 9)
Biomedical Engineering     Hybrid Journal   (Followers: 16)
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: 16)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 31)
Biomedical Engineering: Applications, Basis and Communications     Hybrid Journal   (Followers: 5)
Biomedical Microdevices     Hybrid Journal   (Followers: 8)
Biomedical Science and Engineering     Open Access   (Followers: 3)
Biomedizinische Technik - Biomedical Engineering     Hybrid Journal  
Biomicrofluidics     Open Access   (Followers: 4)
BioNanoMaterials     Hybrid Journal   (Followers: 1)
Biotechnology Progress     Hybrid Journal   (Followers: 39)
Boletin Cientifico Tecnico INIMET     Open Access  
Botswana Journal of Technology     Full-text available via subscription  
Boundary Value Problems     Open Access   (Followers: 1)
Brazilian Journal of Science and Technology     Open Access   (Followers: 2)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 10)
Bulletin of Canadian Petroleum Geology     Full-text available via subscription   (Followers: 14)
Bulletin of Engineering Geology and the Environment     Hybrid Journal   (Followers: 3)
Bulletin of the Crimean Astrophysical Observatory     Hybrid Journal  
Cahiers, Droit, Sciences et Technologies     Open Access  
Calphad     Hybrid Journal  
Canadian Geotechnical Journal     Full-text available via subscription   (Followers: 13)
Canadian Journal of Remote Sensing     Full-text available via subscription   (Followers: 40)
Case Studies in Engineering Failure Analysis     Open Access   (Followers: 7)
Case Studies in Thermal Engineering     Open Access   (Followers: 3)
Catalysis Communications     Hybrid Journal   (Followers: 6)
Catalysis Letters     Hybrid Journal   (Followers: 2)
Catalysis Reviews: Science and Engineering     Hybrid Journal   (Followers: 8)
Catalysis Science and Technology     Free   (Followers: 6)
Catalysis Surveys from Asia     Hybrid Journal   (Followers: 3)
Catalysis Today     Hybrid Journal   (Followers: 5)
CEAS Space Journal     Hybrid Journal  
Cellular and Molecular Neurobiology     Hybrid Journal   (Followers: 3)
Central European Journal of Engineering     Hybrid Journal   (Followers: 1)
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: 1)
CienciaUAT     Open Access  
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: 14)
City, Culture and Society     Hybrid Journal   (Followers: 21)
Clay Minerals     Full-text available via subscription   (Followers: 9)
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Coal Science and Technology     Full-text available via subscription   (Followers: 3)
Coastal Engineering     Hybrid Journal   (Followers: 11)
Coastal Engineering Journal     Hybrid Journal   (Followers: 4)
Coatings     Open Access   (Followers: 2)
Cogent Engineering     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Color Research & Application     Hybrid Journal   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
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: 23)
Composite Interfaces     Hybrid Journal   (Followers: 6)
Composite Structures     Hybrid Journal   (Followers: 252)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 177)
Composites Part B : Engineering     Hybrid Journal   (Followers: 223)
Composites Science and Technology     Hybrid Journal   (Followers: 164)
Comptes Rendus Mécanique     Full-text available via subscription   (Followers: 2)
Computation     Open Access  
Computational Geosciences     Hybrid Journal   (Followers: 12)
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
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Computer Applications in Engineering Education     Hybrid Journal   (Followers: 6)
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Computers & Geosciences     Hybrid Journal   (Followers: 25)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Computers and Electronics in Agriculture     Hybrid Journal   (Followers: 4)
Computers and Geotechnics     Hybrid Journal   (Followers: 8)
Computing and Visualization in Science     Hybrid Journal   (Followers: 6)
Computing in Science & Engineering     Full-text available via subscription   (Followers: 25)
Conciencia Tecnologica     Open Access  
Concurrent Engineering     Hybrid Journal   (Followers: 3)
Continuum Mechanics and Thermodynamics     Hybrid Journal   (Followers: 6)
Control and Dynamic Systems     Full-text available via subscription   (Followers: 8)
Control Engineering Practice     Hybrid Journal   (Followers: 41)
Control Theory and Informatics     Open Access   (Followers: 7)
Corrosion Science     Hybrid Journal   (Followers: 24)
CT&F Ciencia, Tecnologia y Futuro     Open Access  
CTheory     Open Access  

        1 2 3 4 5 6 | 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  [2329 journals]
  • Second-order orthant-based methods with enriched Hessian information for
           sparse $$\ell _1$$ ℓ 1 -optimization
    • Authors: J. C. De Los Reyes; E. Loayza; P. Merino
      Pages: 225 - 258
      Abstract: We present a second order algorithm, based on orthantwise directions, for solving optimization problems involving the sparsity enhancing \(\ell _1\) -norm. The main idea of our method consists in modifying the descent orthantwise directions by using second order information both of the regular term and (in weak sense) of the \(\ell _1\) -norm. The weak second order information behind the \(\ell _1\) -term is incorporated via a partial Huber regularization. One of the main features of our algorithm consists in a faster identification of the active set. We also prove that a reduced version of our method is equivalent to a semismooth Newton algorithm applied to the optimality condition, under a specific choice of the algorithm parameters. We present several computational experiments to show the efficiency of our approach compared to other state-of-the-art algorithms.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9891-z
      Issue No: Vol. 67, No. 2 (2017)
       
  • Local and global convergence of a general inertial proximal splitting
           scheme for minimizing composite functions
    • Authors: Patrick R. Johnstone; Pierre Moulin
      Pages: 259 - 292
      Abstract: This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally inexpensive proximal operator. We analyze a family of generalized inertial proximal splitting algorithms (GIPSA) for solving such problems. We establish weak convergence of the generated sequence when the minimum is attained. Our analysis unifies and extends several previous results. We then focus on \(\ell _1\) -regularized optimization, which is the ubiquitous special case where the nonsmooth term is the \(\ell _1\) -norm. For certain parameter choices, GIPSA is amenable to a local analysis for this problem. For these choices we show that GIPSA achieves finite “active manifold identification”, i.e. convergence in a finite number of iterations to the optimal support and sign, after which GIPSA reduces to minimizing a local smooth function. We prove local linear convergence under either restricted strong convexity or a strict complementarity condition. We determine the rate in terms of the inertia, stepsize, and local curvature. Our local analysis is applicable to certain recent variants of the Fast Iterative Shrinkage–Thresholding Algorithm (FISTA), for which we establish active manifold identification and local linear convergence. Based on our analysis we propose a momentum restart scheme in these FISTA variants to obtain the optimal local linear convergence rate while maintaining desirable global properties.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9896-7
      Issue No: Vol. 67, No. 2 (2017)
       
  • Branch-and-price for p -cluster editing
    • Authors: Teobaldo Bulhões; Anand Subramanian; Gilberto F. Sousa Filho; Lucídio dos Anjos F. Cabral
      Pages: 293 - 316
      Abstract: Given an input graph, the p-cluster editing problem consists of minimizing the number of editions, i.e., additions and/or deletions of edges, so as to create p vertex-disjoint cliques (clusters). In order to solve this \({\mathscr {NP}}\) -hard problem, we propose a branch-and-price algorithm over a set partitioning based formulation with exponential number of variables. We show that this formulation theoretically dominates the best known formulation for the problem. Moreover, we compare the performance of three mathematical formulations for the pricing subproblem, which is strongly \({\mathscr {NP}}\) -hard. A heuristic algorithm is also proposed to speedup the column generation procedure. We report improved bounds for benchmark instances available in the literature.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9893-x
      Issue No: Vol. 67, No. 2 (2017)
       
  • Solving nearly-separable quadratic optimization problems as nonsmooth
           equations
    • Authors: Frank E. Curtis; Arvind U. Raghunathan
      Pages: 317 - 360
      Abstract: An algorithm for solving nearly-separable quadratic optimization problems (QPs) is presented. The approach is based on applying a semismooth Newton method to solve the implicit complementarity problem arising as the first-order stationarity conditions of such a QP. An important feature of the approach is that, as in dual decomposition methods, separability of the dual function of the QP can be exploited in the search direction computation. Global convergence of the method is promoted by enforcing decrease in component(s) of a Fischer–Burmeister formulation of the complementarity conditions, either via a merit function or through a filter mechanism. The results of numerical experiments when solving convex and nonconvex instances are provided to illustrate the efficacy of the method.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9895-8
      Issue No: Vol. 67, No. 2 (2017)
       
  • An SQP method for mathematical programs with vanishing constraints with
           strong convergence properties
    • Authors: Matúš Benko; Helmut Gfrerer
      Pages: 361 - 399
      Abstract: We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of \({\mathcal {Q}}\) -stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how \({\mathcal {Q}}_M\) -stationary solutions of the quadratic program can be obtained. We show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method we also guarantee the stronger property of \({\mathcal {Q}}_M\) -stationarity of the limit points.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9894-9
      Issue No: Vol. 67, No. 2 (2017)
       
  • $$L^1$$ L 1 penalization of volumetric dose objectives in optimal control
           of PDEs
    • Authors: Richard C. Barnard; Christian Clason
      Pages: 401 - 419
      Abstract: This work is concerned with a class of PDE-constrained optimization problems that are motivated by an application in radiotherapy treatment planning. Here the primary design objective is to minimize the volume where a functional of the state violates a prescribed level, but prescribing these levels in the form of pointwise state constraints leads to infeasible problems. We therefore propose an alternative approach based on \(L^1\) penalization of the violation that is also applicable when state constraints are infeasible. We establish well-posedness of the corresponding optimal control problem, derive first-order optimality conditions, discuss convergence of minimizers as the penalty parameter tends to infinity, and present a semismooth Newton method for their efficient numerical solution. The performance of this method for a model problem is illustrated and contrasted with an alternative approach based on (regularized) state constraints.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9897-6
      Issue No: Vol. 67, No. 2 (2017)
       
  • Visualization of the $$\varepsilon $$ ε -subdifferential of piecewise
           linear–quadratic functions
    • Authors: Anuj Bajaj; Warren Hare; Yves Lucet
      Pages: 421 - 442
      Abstract: Computing explicitly the \(\varepsilon \) -subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) piecewise linear–quadratic functions for which existing numerical libraries allow practical computations. We visualize the results in a primal, dual, and subdifferential views through several numerical examples. We also provide a visualization of the Brøndsted–Rockafellar theorem.
      PubDate: 2017-06-01
      DOI: 10.1007/s10589-017-9892-y
      Issue No: Vol. 67, No. 2 (2017)
       
  • Error estimates for integral constraint regularization of
           state-constrained elliptic control problems
    • Authors: B. Jadamba; A. Khan; M. Sama
      Pages: 39 - 71
      Abstract: In this paper, we study new aspects of the integral contraint regularization of state-constrained elliptic control problems (Jadamba et al. in Syst Control Lett 61(6):707–713, 2012). Besides giving new results on the regularity and the convergence of the regularized controls and associated Lagrange multipliers, the main objective of this paper is to give abstract error estimates for the regularization error. We also consider a discretization of the regularized problems and derive numerical estimates which are uniform with respect to the regularization parameter and the discretization parameter. As an application of these results, we prove that this discretization is indeed a full discretization of the original problem defined in terms of a problem with finitely many integral constraints. Detailed numerical results justifying the theoretical findings as well as a comparison of our work with the existing literature is also given.
      PubDate: 2017-05-01
      DOI: 10.1007/s10589-016-9885-2
      Issue No: Vol. 67, No. 1 (2017)
       
  • A new approach for finding a basis for the splitting preconditioner for
           linear systems from interior point methods
    • Authors: Porfirio Suñagua; Aurelio R. L. Oliveira
      Pages: 111 - 127
      Abstract: The class of splitting preconditioners for the iterative solution of linear systems arising from Mehrotra’s predictor-corrector method for large scale linear programming problems needs to find a basis through a sophisticated process based on the application of a rectangular LU factorization. This class of splitting preconditioners works better near a solution of the linear programming problem when the matrices are highly ill-conditioned. In this study, we develop and implement a new approach to find a basis for the splitting preconditioner, based on standard rectangular LU factorization with partial permutation of the scaled transpose linear programming constraint matrix. In most cases, this basis is better conditioned than the existing one. In addition, we include a penalty parameter in Mehrotra’s predictor-corrector method in order to reduce ill-conditioning of the normal equations matrix. Computational experiments show a reduction in the average number of iterations of the preconditioned conjugate gradient method. Also, the increased efficiency and robustness of the new approach become evident by the performance profile.
      PubDate: 2017-05-01
      DOI: 10.1007/s10589-016-9887-0
      Issue No: Vol. 67, No. 1 (2017)
       
  • On merit functions for p -order cone complementarity problem
    • Authors: Xin-He Miao; Yu-Lin Chang; Jein-Shan Chen
      Pages: 155 - 173
      Abstract: Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.
      PubDate: 2017-05-01
      DOI: 10.1007/s10589-016-9889-y
      Issue No: Vol. 67, No. 1 (2017)
       
  • Analysis on Newton projection method for the split feasibility problem
    • Authors: Biao Qu; Changyu Wang; Naihua Xiu
      Pages: 175 - 199
      Abstract: In this paper, based on a merit function of the split feasibility problem (SFP), we present a Newton projection method for solving it and analyze the convergence properties of the method. The merit function is differentiable and convex. But its gradient is a linear composite function of the projection operator, so it is nonsmooth in general. We prove that the sequence of iterates converges globally to a solution of the SFP as long as the regularization parameter matrix in the algorithm is chosen properly. Especially, under some local assumptions which are necessary for the case where the projection operator is nonsmooth, we prove that the sequence of iterates generated by the algorithm superlinearly converges to a regular solution of the SFP. Finally, some numerical results are presented.
      PubDate: 2017-05-01
      DOI: 10.1007/s10589-016-9884-3
      Issue No: Vol. 67, No. 1 (2017)
       
  • Generalized Krasnoselskii–Mann-type iterations for nonexpansive
           mappings in Hilbert spaces
    • Abstract: The Krasnoselskii–Mann iteration plays an important role in the approximation of fixed points of nonexpansive operators; it is known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a new inexact Krasnoselskii–Mann iteration and prove weak convergence under certain accuracy criteria on the error resulting from the inexactness. We also show strong convergence for a modified inexact Krasnoselskii–Mann iteration under suitable assumptions. The convergence results generalize existing ones from the literature. Applications are given to the Douglas–Rachford splitting method, the Fermat–Weber location problem as well as the alternating projection method by John von Neumann.
      PubDate: 2017-07-01
       
  • $$S_{1/2}$$ S 1 / 2 regularization methods and fixed point algorithms for
           affine rank minimization problems
    • Abstract: The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unlike the literatures which use the nuclear norm or the general Schatten \(q~ (0<q<1)\) quasi-norm to approximate the rank of a matrix, in this paper we use the Schatten 1 / 2 quasi-norm approximation which is a better approximation than the nuclear norm but leads to a nonconvex, nonsmooth and non-Lipschitz optimization problem. It is important that we give a global necessary optimality condition for the \(S_{1/2}\) regularization problem by virtue of the special objective function. This is very different from the local optimality conditions usually used for the general \(S_q\) regularization problems. Explicitly, the global necessary optimality condition for the \(S_{1/2}\) regularization problem is a fixed point inclusion associated with the singular value half thresholding operator. Naturally, we propose a fixed point iterative scheme for the problem. We also provide the convergence analysis of this iteration. By discussing the location and setting of the optimal regularization parameter as well as using an approximate singular value decomposition procedure, we get a very efficient algorithm, half norm fixed point algorithm with an approximate SVD (HFPA algorithm), for the \(S_{1/2}\) regularization problem. Numerical experiments on randomly generated and real matrix completion problems are presented to demonstrate the effectiveness of the proposed algorithm.
      PubDate: 2017-07-01
       
  • Further properties of the forward–backward envelope with applications to
           difference-of-convex programming
    • Abstract: In this paper, we further study the forward–backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE Conference on Decision and Control, pp 2358–2363, 2013) and Stella et al. (Comput Optim Appl, doi:10.1007/s10589-017-9912-y, 2017) for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forward–backward envelope to be a level-bounded and Kurdyka–Łojasiewicz function with an exponent of \(\frac{1}{2}\) ; these results are important for the efficient minimization of the forward–backward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some difference-of-convex regularized least squares problems by minimizing a suitably constructed forward–backward envelope. Our preliminary numerical results on randomly generated instances of large-scale \(\ell _{1-2}\) regularized least squares problems (Yin et al. in SIAM J Sci Comput 37:A536–A563, 2015) illustrate that an implementation of this approach with a limited-memory BFGS scheme usually outperforms standard first-order methods such as the nonmonotone proximal gradient method in Wright et al. (IEEE Trans Signal Process 57:2479–2493, 2009).
      PubDate: 2017-07-01
       
  • Forward–backward quasi-Newton methods for nonsmooth optimization
           problems
    • Abstract: The forward–backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward–backward envelope (FBE). This allows to extend algorithms for smooth unconstrained optimization and apply them to nonsmooth (possibly constrained) problems. Since the FBE can be computed by simply evaluating forward–backward steps, the resulting methods rely on a similar black-box oracle as FBS. We propose an algorithmic scheme that enjoys the same global convergence properties of FBS when the problem is convex, or when the objective function possesses the Kurdyka–Łojasiewicz property at its critical points. Moreover, when using quasi-Newton directions the proposed method achieves superlinear convergence provided that usual second-order sufficiency conditions on the FBE hold at the limit point of the generated sequence. Such conditions translate into milder requirements on the original function involving generalized second-order differentiability. We show that BFGS fits our framework and that the limited-memory variant L-BFGS is well suited for large-scale problems, greatly outperforming FBS or its accelerated version in practice, as well as ADMM and other problem-specific solvers. The analysis of superlinear convergence is based on an extension of the Dennis and Moré theorem for the proposed algorithmic scheme.
      PubDate: 2017-07-01
       
  • New subgradient extragradient methods for common solutions to equilibrium
           problems
    • Abstract: In this paper, three parallel hybrid subgradient extragradient algorithms are proposed for finding a common solution of a finite family of equilibrium problems in Hilbert spaces. The proposed algorithms originate from previously known results for variational inequalities and can be considered as modifications of extragradient methods for equilibrium problems. Theorems of strong convergence are established under the standard assumptions imposed on bifunctions. Some numerical experiments are given to illustrate the convergence of the new algorithms and to compare their behavior with other algorithms.
      PubDate: 2017-07-01
       
  • Total variation image deblurring with space-varying kernel
    • Abstract: Image deblurring techniques based on convex optimization formulations, such as total-variation deblurring, often use specialized first-order methods for large-scale nondifferentiable optimization. A key property exploited in these methods is spatial invariance of the blurring operator, which makes it possible to use the fast Fourier transform (FFT) when solving linear equations involving the operator. In this paper we extend this approach to two popular models for space-varying blurring operators, the Nagy–O’Leary model and the efficient filter flow model. We show how splitting methods derived from the Douglas–Rachford algorithm can be implemented with a low complexity per iteration, dominated by a small number of FFTs.
      PubDate: 2017-07-01
       
  • A generalized elastic net regularization with smoothed $$\ell _{q}$$ ℓ q
           penalty for sparse vector recovery
    • Authors: Yong Zhang; Wanzhou Ye; Jianjun Zhang
      Abstract: In this paper, we propose an iterative algorithm for solving the generalized elastic net regularization problem with smoothed \(\ell _{q} (0<q \le 1)\) penalty for recovering sparse vectors. We prove the convergence result of the algorithm based on the algebraic method. Under certain conditions, we show that the iterative solutions converge to a local minimizer of the generalized elastic net regularization problem and we also present an error bound. Theoretical analysis and numerical results show that the proposed algorithm is promising.
      PubDate: 2017-05-18
      DOI: 10.1007/s10589-017-9916-7
       
  • Peaceman–Rachford splitting for a class of nonconvex optimization
           problems
    • Authors: Guoyin Li; Tianxiang Liu; Ting Kei Pong
      Abstract: We study the applicability of the Peaceman–Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is computable, then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem. We also give sufficient conditions guaranteeing boundedness of the sequence generated. We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems with a coercive objective that is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function; this setting covers a large class of nonconvex feasibility problems and constrained least squares problems. Finally, we illustrate the proposed algorithm numerically.
      PubDate: 2017-05-13
      DOI: 10.1007/s10589-017-9915-8
       
  • An exact algorithm for a resource allocation problem in mobile wireless
           communications
    • Authors: Adam N. Letchford; Qiang Ni; Zhaoyu Zhong
      Abstract: We consider a challenging resource allocation problem arising in mobile wireless communications. The goal is to allocate the available channels and power in a so-called OFDMA system, in order to maximise the transmission rate, subject to quality of service constraints. Standard MINLP software struggled to solve even small instances of this problem. Using outer approximation, perspective cuts and several implementation “tricks”, we are able to solve realistic instances in about one minute. A novel ingredient of our algorithm is what we call pre-emptive cut generation: the generation of cutting planes that are not violated in the current iteration, but are likely to be violated in subsequent iterations.
      PubDate: 2017-05-05
      DOI: 10.1007/s10589-017-9914-9
       
 
 
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