Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 43)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 20)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 21)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 6)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 15)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 2)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 20)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 10)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Computational Optimization and Applications
Journal Prestige (SJR): 1.127
Citation Impact (citeScore): 2
Number of Followers: 9  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-2894 - ISSN (Online) 0926-6003
Published by Springer-Verlag Homepage  [2467 journals]
  • Solving constrained nonsmooth group sparse optimization via group Capped-
           $$\ell _1$$ relaxation and group smoothing proximal gradient algorithm

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      Abstract: Abstract In this paper, we study the constrained group sparse regularization optimization problem, where the loss function is convex but nonsmooth, and the penalty term is the group sparsity which is then proposed to be relaxed by the group Capped- \(\ell _1\) for the convenience of computation. Firstly, we introduce three kinds of stationary points for the continuous relaxation problem and describe the relationship of the three kinds of stationary points. We give the optimality conditions for the group Capped- \(\ell _1\) problem and the original group sparse regularization problem, and investigate the link between the relaxation problem and the original problem in terms of global and local optimal solutions. The results reveal the equivalence of the original problem and the relaxation problem in some sense. Secondly, we propose a group smoothing proximal gradient (GSPG) algorithm for the constrained group sparse optimization, and prove that the proposed GSPG algorithm globally converges to a lifted stationary point of the relaxation problem. Finally, we present some numerical results on recovery of the simulated group sparse signals and the real group sparse images to illustrate the efficiency of the continuous relaxation model and the proposed algorithm.
      PubDate: 2022-12-01
       
  • A stabilized sequential quadratic semidefinite programming method for
           degenerate nonlinear semidefinite programs

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      Abstract: Abstract In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic semidefinite programming (QSDP) subproblems, which we derive from the minimax problem associated with the NSDP. Unlike the existing SQSDP methods, the proposed one allows us to solve those QSDP subproblems inexactly, and each QSDP is feasible. One more remarkable point of the proposed method is that constraint qualifications or boundedness of Lagrange multiplier sequences are not required in the global convergence analysis. Specifically, without assuming such conditions, we prove the global convergence to a point satisfying any of the following: the stationary conditions for the feasibility problem, the approximate-Karush–Kuhn–Tucker (AKKT) conditions, and the trace-AKKT conditions. Finally, we conduct some numerical experiments to examine the efficiency of the proposed method.
      PubDate: 2022-12-01
       
  • Completely positive factorization by a Riemannian smoothing method

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      Abstract: Abstract Copositive optimization is a special case of convex conic programming, and it consists of optimizing a linear function over the cone of all completely positive matrices under linear constraints. Copositive optimization provides powerful relaxations of NP-hard quadratic problems or combinatorial problems, but there are still many open problems regarding copositive or completely positive matrices. In this paper, we focus on one such problem; finding a completely positive (CP) factorization for a given completely positive matrix. We treat it as a nonsmooth Riemannian optimization problem, i.e., a minimization problem of a nonsmooth function over a Riemannian manifold. To solve this problem, we present a general smoothing framework for solving nonsmooth Riemannian optimization problems and show convergence to a stationary point of the original problem. An advantage is that we can implement it quickly with minimal effort by directly using the existing standard smooth Riemannian solvers, such as Manopt. Numerical experiments show the efficiency of our method especially for large-scale CP factorizations.
      PubDate: 2022-12-01
       
  • Computable centering methods for spiraling algorithms and their duals,
           with motivations from the theory of Lyapunov functions

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      Abstract: Abstract For many problems, some of which are reviewed in the paper, popular algorithms like Douglas–Rachford (DR), ADMM, and FISTA produce approximating sequences that show signs of spiraling toward the solution. We present a meta-algorithm that exploits such dynamics to potentially enhance performance. The strategy of this meta-algorithm is to iteratively build and minimize surrogates for the Lyapunov function that captures those dynamics. As a first motivating application, we show that for prototypical feasibility problems the circumcentered-reflection method, subgradient projections, and Newton–Raphson are all describable as gradient-based methods for minimizing Lyapunov functions constructed for DR operators, with the former returning the minimizers of spherical surrogates for the Lyapunov function. As a second motivating application, we introduce a new method that shares these properties but with the added advantages that it: (1) does not rely on subproblems (e.g. reflections) and so may be applied for any operator whose iterates have the spiraling property; (2) provably has the aforementioned Lyapunov properties with few structural assumptions and so is generically suitable for primal/dual implementation; and (3) maps spaces of reduced dimension into themselves whenever the original operator does. This makes possible the first primal/dual implementation of a method that seeks the center of spiraling iterates. We describe this method, and provide a computed example (basis pursuit).
      PubDate: 2022-12-01
       
  • New Bregman proximal type algorithms for solving DC optimization
           problems

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      Abstract: Abstract Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of the objective function have L-smoothness. In this article, we propose the Bregman Proximal DC Algorithm (BPDCA) for solving large-scale DC optimization problems that do not possess L-smoothness. Instead, it requires that the convex part of the objective function has the L-smooth adaptable property that is exploited in Bregman proximal gradient algorithms. In addition, we propose an accelerated version, the Bregman Proximal DC Algorithm with extrapolation (BPDCAe), with a new restart scheme. We show the global convergence of the iterates generated by BPDCA(e) to a limiting critical point under the assumption of the Kurdyka-Łojasiewicz property or subanalyticity of the objective function and other weaker conditions than those of the existing methods. We applied our algorithms to phase retrieval, which can be described both as a nonconvex optimization problem and as a DC optimization problem. Numerical experiments showed that BPDCAe outperformed existing Bregman proximal-type algorithms because the DC formulation allows for larger admissible step sizes.
      PubDate: 2022-12-01
       
  • An extrapolated iteratively reweighted $$\ell _1$$ method with complexity
           analysis

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      Abstract: Abstract The iteratively reweighted \(\ell _1\) algorithm is a widely used method for solving various regularization problems, which generally minimize a differentiable loss function combined with a convex/nonconvex regularizer to induce sparsity in the solution. However, the convergence and the complexity of iteratively reweighted \(\ell _1\) algorithms is generally difficult to analyze, especially for non-Lipschitz differentiable regularizers such as \(\ell _p\) norm regularization with \(0<p<1\) . In this paper, we propose, analyze and test a reweighted \(\ell _1\) algorithm combined with the extrapolation technique under the assumption of Kurdyka-Łojasiewicz (KL) property on the proximal function of the perturbed objective. Our method does not require the Lipschitz differentiability on the regularizers nor the smoothing parameters in the weights bounded away from 0. We show the proposed algorithm converges uniquely to a stationary point of the regularization problem and has local linear convergence for KL exponent at most 1/2 and local sublinear convergence for KL exponent greater than 1/2. We also provide results on calculating the KL exponents and discuss the cases when the KL exponent is at most 1/2. Numerical experiments show the efficiency of our proposed method.
      PubDate: 2022-12-01
       
  • A two-level distributed algorithm for nonconvex constrained optimization

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      Abstract: This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the recent development of distributed algorithms for nonconvex programs, highly complicated constraints still pose a significant challenge in theory and practice. We first identify some difficulties with the existing algorithms based on the alternating direction method of multipliers (ADMM) for dealing with such problems. We then propose a reformulation that enables us to design a two-level algorithm, which embeds a specially structured three-block ADMM at the inner level in an augmented Lagrangian method framework. Furthermore, we prove the global and local convergence as well as iteration complexity of this new scheme for general nonconvex constrained programs, and show that our analysis can be extended to handle more complicated multi-block inner-level problems. Finally, we demonstrate with computation that the new scheme provides convergent and parallelizable algorithms for various nonconvex applications, and is able to complement the performance of the state-of-the-art distributed algorithms in practice by achieving either faster convergence in optimality gap or in feasibility or both.
      PubDate: 2022-11-23
       
  • Distributed stochastic gradient tracking methods with momentum
           acceleration for non-convex optimization

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      Abstract: Abstract We consider a distributed non-convex optimization problem of minimizing the sum of all local cost functions over a network of agents. This problem often appears in large-scale distributed machine learning, known as non-convex empirical risk minimization. In this paper, we propose two accelerated algorithms, named DSGT-HB and DSGT-NAG, which combine the distributed stochastic gradient tracking (DSGT) method with momentum accelerated techniques. Under appropriate assumptions, we prove that both algorithms sublinearly converge to a neighborhood of a first-order stationary point of the distributed non-convex optimization. Moreover, we derive the conditions under which DSGT-HB and DSGT-NAG achieve a network-independent linear speedup. Numerical experiments for a distributed non-convex logistic regression problem on real data sets and a deep neural network on the MNIST database show the superiorities of DSGT-HB and DSGT-NAG compared with DSGT.
      PubDate: 2022-11-23
       
  • Special issue for SIMAI 2020–2021: large-scale optimization and
           applications

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      PubDate: 2022-11-22
       
  • Correction to: Differentiability results and sensitivity calculation for
           optimal control of incompressible two-phase Navier–Stokes equations with
           surface tension

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      PubDate: 2022-11-15
       
  • General-purpose preconditioning for regularized interior point methods

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      Abstract: Abstract In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.
      PubDate: 2022-11-14
       
  • Modeling design and control problems involving neural network surrogates

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      Abstract: Abstract We consider nonlinear optimization problems that involve surrogate models represented by neural networks. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific case of feedforward neural networks with ReLU activation: as a mixed-integer optimization problem and as a mathematical program with complementarity constraints. For the latter formulation we prove that stationarity at a point for this problem corresponds to stationarity of the embedded formulation. Each of these formulations may be solved with state-of-the-art optimization methods, and we show how to obtain good initial feasible solutions for these methods. We compare our formulations on three practical applications arising in the design and control of combustion engines, in the generation of adversarial attacks on classifier networks, and in the determination of optimal flows in an oil well network.
      PubDate: 2022-11-14
       
  • COAP 2021 Best Paper Prize

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      PubDate: 2022-11-10
       
  • On the SCD semismooth* Newton method for generalized equations with
           application to a class of static contact problems with Coulomb friction

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      Abstract: Abstract In the paper, a variant of the semismooth \(^{*}\) Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild regularity requirement, the method exhibits (locally) superlinear convergence behavior. From the main conceptual algorithm, two implementable variants are derived whose efficiency is tested via a generalized equation modeling a discretized static contact problem with Coulomb friction.
      PubDate: 2022-11-07
       
  • A global exact penalty for rank-constrained optimization problem and
           applications

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      Abstract: Abstract This paper considers a rank-constrained optimization problem where the objective function is continuously differentiable on a closed convex set. After replacing the rank constraint by an equality of the truncated difference of L1 and L2 norm, and adding the equality constraint into the objective to get a penalty problem, we prove that the penalty problem is exact in the sense that the set of its global (local) optimal solutions coincides with that of the original problem when the penalty parameter is over a certain threshold. This establishes the theoretical guarantee for the truncated difference of L1 and L2 norm regularization optimization including the work of Ma et al. (SIAM J Imaging Sci 10(3):1346–1380, 2017). Besides, for the penalty problem, we propose an extrapolation proximal difference of convex algorithm (epDCA) and prove the sequence generated by epDCA converges to a stationary point of the penalty problem. Further, an adaptive penalty method based on epDCA is constructed for the original rank-constrained problem. The efficiency of the algorithms is verified via numerical experiments for the nearest low-rank correlation matrix problem and the matrix completion problem.
      PubDate: 2022-11-05
       
  • On FISTA with a relative error rule

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      Abstract: Abstract The fast iterative shrinkage/thresholding algorithm (FISTA) is one of the most popular first-order iterations for minimizing the sum of two convex functions. FISTA is known to improve the complexity of the classical proximal gradient method (PGM) from \(O(k^{-1})\) to the optimal complexity \(O(k^{-2})\) in terms of the sequence of the functional values. When the evaluation of the proximal operator is hard, inexact versions of FISTA might be used to solve the problem. In this paper, we proposed an inexact version of FISTA by solving the proximal subproblem inexactly using a relative error criterion instead of exogenous and diminishing error rules. The introduced relative error rule in the FISTA iteration is related to the progress of the algorithm at each step and does not increase the computational burden per iteration. Moreover, the proposed algorithm recovers the same optimal convergence rate as FISTA. Some numerical experiments are also reported to illustrate the numerical behavior of the relative inexact method when compared with FISTA under an absolute error criterion.
      PubDate: 2022-11-04
       
  • A stochastic first-order trust-region method with inexact restoration for
           finite-sum minimization

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      Abstract: Abstract We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved.
      PubDate: 2022-11-03
       
  • “FISTA” in Banach spaces with adaptive discretisations

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      Abstract: Abstract FISTA is a popular convex optimisation algorithm which is known to converge at an optimal rate whenever a minimiser is contained in a suitable Hilbert space. We propose a modified algorithm where each iteration is performed in a subset which is allowed to change at every iteration. Sufficient conditions are provided for guaranteed convergence, although at a reduced rate depending on the conditioning of the specific problem. These conditions have a natural interpretation when a minimiser exists in an underlying Banach space. Typical examples are L1-penalised reconstructions where we provide detailed theoretical and numerical analysis.
      PubDate: 2022-11-02
       
  • Efficient scalarization in multiobjective optimal control of a nonsmooth
           PDE

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      Abstract: Abstract This work deals with the efficient numerical characterization of Pareto stationary fronts for multiobjective optimal control problems with a moderate number of cost functionals and a mildly nonsmooth, elliptic, semilinear PDE-constraint. When “ample” controls are considered, strong stationarity conditions that can be used to numerically characterize the Pareto stationary fronts are known for our problem. We show that for finite dimensional controls, a sufficient adjoint-based stationarity system remains obtainable. It turns out that these stationarity conditions remain useful when numerically characterizing the fronts, because they correspond to strong stationarity systems for problems obtained by application of weighted-sum and reference point techniques to the multiobjective problem. We compare the performance of both scalarization techniques using quantifiable measures for the approximation quality. The subproblems of either method are solved with a line-search globalized pseudo-semismooth Newton method that appears to remove the degenerate behavior of the local version of the method employed previously. We apply a matrix-free, iterative approach to deal with the memory and complexity requirements when solving the subproblems of the reference point method and compare several preconditioning approaches.
      PubDate: 2022-08-28
      DOI: 10.1007/s10589-022-00390-y
       
  • Minimization over the $$\ell _1$$ ℓ 1 -ball using an active-set
           non-monotone projected gradient

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      Abstract: Abstract The \(\ell _1\) -ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the \(\ell _1\) -ball and embed it into a tailored algorithmic scheme that makes use of a non-monotone first-order approach to explore the given subspace at each iteration. We prove global convergence to stationary points. Finally, we report numerical experiments, on two different classes of instances, showing the effectiveness of the algorithm.
      PubDate: 2022-08-27
      DOI: 10.1007/s10589-022-00407-6
       
 
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