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algorithm (193) 193
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inequalities (119) 119
computer science (116) 116
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computation (94) 94
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quadratic programming (72) 72
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regularization (67) 67
real functions (64) 64
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algebra (58) 58
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nonlinear equations (57) 57
conjugate gradient method (56) 56
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lagrange multiplier (42) 42
management science (42) 42
numeric computing (42) 42
penalty function (42) 42
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1. Full Text A family of second-order methods for convex ℓ1 -regularized optimization
by Byrd, Richard H and Chin, Gillian M and Nocedal, Jorge and Oztoprak, Figen
Mathematical Programming, ISSN 0025-5610, 09/2016, Volume 159, Issue 1-2, pp. 435 - 467
65K05 | 90C30 | 49M37
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2. Full Text Proximal alternating linearized minimization for nonconvex and nonsmooth problems
by Bolte, Jérôme and Bolte, Jérôme and Sabach, Shoham and Sabach, Shoham and Teboulle, Marc and Teboulle, Marc
Mathematical Programming, ISSN 0025-5610, 8/2014, Volume 146, Issue 1, pp. 459 - 494
We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems.... 
Gauss-Seidel method | Kurdyka–Łojasiewicz property | Theoretical, Mathematical and Computational Physics | Block coordinate descent | Alternating minimization | Mathematics | 90C26 | Nonconvex-nonsmooth minimization | Proximal forward-backward | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 65K10 | 49M27 | 49M37 | Combinatorics | 47J25 | Sparse nonnegative matrix factorization | Kurdyka-Łojasiewicz property | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | Kurdyka-Lojasiewicz property | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | CONSTRAINTS | NONNEGATIVE MATRIX FACTORIZATION | LOJASIEWICZ INEQUALITY | Analysis | Management science | Algorithms | Studies | Data smoothing | Mathematical programming | Functions (mathematics) | Construction | Mathematical analysis | Palm | Byproducts | Minimization | Optimization | Optimization and Control
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3. Full Text A note on scalar "generalized" invexity
by Cambini, Riccardo and Carosi, Laura
Journal of Information and Optimization Sciences, ISSN 0252-2667, 04/2019, Volume 40, Issue 3, pp. 615 - 632
This paper aims to study how much "generalized" invex properties differ from invexity and to establish whether or not the use of more and more parameters and... 
90C26 | 90C30 | 90C46 | Generalized convexity | generalized invexity
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4. Full Text On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers
by He, Bingsheng and He, Bingsheng and Yuan, Xiaoming and Yuan, Xiaoming
Numerische Mathematik, ISSN 0029-599X, 7/2015, Volume 130, Issue 3, pp. 567 - 577
This note proposes a novel approach to derive a worst-case $$O(1/k)$$ O ( 1 / k ) convergence rate measured by the iteration complexity in a non-ergodic sense... 
Mathematical Methods in Physics | 90C30 | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | MATHEMATICS, APPLIED | Yuan (China) | Methods
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5. Full Text The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent
by Chen, Caihua and Chen, Caihua and He, Bingsheng and He, Bingsheng and Ye, Yinyu and Ye, Yinyu and Yuan, Xiaoming and Yuan, Xiaoming
Mathematical Programming, ISSN 0025-5610, 1/2016, Volume 155, Issue 1, pp. 57 - 79
The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are... 
Alternating direction method of multipliers | Theoretical, Mathematical and Computational Physics | Mathematics | Convex programming | Convergence analysis | Mathematical Methods in Physics | Splitting methods | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 65K13 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Yuan (China) | Management techniques | Management science | Management | Analysis | Studies | Mathematical analysis | Convex analysis | Convergence | Mathematical programming | Functions (mathematics) | Multipliers | Divergence | Minimization | Optimization
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6. Full Text Minimizing finite sums with the stochastic average gradient
by Schmidt, Mark and Schmidt, Mark and Le Roux, Nicolas and Le Roux, Nicolas and Bach, Francis and Bach, Francis
Mathematical Programming, ISSN 0025-5610, 3/2017, Volume 162, Issue 1, pp. 83 - 112
We analyze the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG)... 
68Q25 | 65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Stochastic gradient methods | 90C15 | First-order methods | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Convergence Rates | Combinatorics | 62L20 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | ALGORITHMS | Analysis | Algorithms | Studies | Convex analysis | Optimization | Mathematical analysis | Sag | Texts | Strategy | Mathematical models | Stochasticity | Sampling | Convergence
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7. Full Text On the solution of quadratic programming problem with a feasible region defined as a Minkowski sum of a compact set and finitely generated convex closed cone
by Stefanov, Stefan M
Journal of Information and Optimization Sciences, ISSN 0252-2667, 08/2018, Volume 39, Issue 6, pp. 1223 - 1230
Quadratic programming problem with bounded below (bounded above, respectively) quadratic objective function over a feasible region, defined as Minkowski sum of... 
90C20 | 90C30 | Quadratic programming | Existence of solution
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8. Full Text A feasible method for optimization with orthogonality constraints
by Wen, Zaiwen and Wen, Zaiwen and Yin, Wotao and Yin, Wotao
Mathematical Programming, ISSN 0025-5610, 12/2013, Volume 142, Issue 1, pp. 397 - 434
Minimization with orthogonality constraints (e.g., $$X^\top X = I$$ ) and/or spherical constraints (e.g., $$\Vert x\Vert _2 = 1$$ ) has wide applications in... 
Nearest correlation matrix | Invariant subspace | 65K05 | Theoretical, Mathematical and Computational Physics | Curvilinear search | Maxcut SDP | Mathematics | 90C26 | Eigenvalue and eigenvector | Quadratic assignment problem | 90C27 | Orthogonality constraint | Mathematical Methods in Physics | Cayley transformation | 90C30 | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Stiefel manifold | Numerical Analysis | 90C22 | Spherical constraint | 49Q99 | Combinatorics | MATHEMATICS, APPLIED | ALGORITHM | DECOMPOSITION | FORMULATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | BARZILAI | MATRICES | RANK REDUCTION | FLOWS | SEMIDEFINITE PROGRAMS | Methods | Algorithms | Studies | Polynomials | Topological manifolds | Analysis | Optimization | Mathematical programming
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9. Full Text On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
by Wächter, Andreas and Wächter, Andreas and Biegler, Lorenz T and Biegler, Lorenz T
Mathematical Programming, ISSN 0025-5610, 3/2006, Volume 106, Issue 1, pp. 25 - 57
We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this... 
65K05 | Mathematical and Computational Physics | Mathematics | Optimization | Filter method | Nonconvex constrained optimization | Line search | Mathematical Methods in Physics | 90C51 | Barrier method | 90C30 | Mathematics of Computing | Numerical Analysis | Calculus of Variations and Optimal Control | Nonlinear programming | 49M37 | Combinatorics | Interior-point method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | interior-point method | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | nonlinear programming | nonconvex constrained optimization | CONSTRAINED OPTIMIZATION | filter method | line search | GLOBAL CONVERGENCE | Algorithms | Comparative studies | Convergence | Heuristic
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10. Full Text A feasible direction algorithm for nonlinear second-order cone programs
by Canelas, Alfredo and Carrasco, Miguel and López, Julio
Optimization Methods and Software, ISSN 1055-6788, 11/2019, Volume 34, Issue 6, pp. 1322 - 1341
In this work, we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These consist of minimizing a nonlinear... 
Second-order cone programming | Feasible direction | Interior-point methods | 90C51 | 90C30 | 49M15 | Support vector machines | Algorithms
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11. Full Text Worst-Case Examples for Lasserre’s Measure–Based Hierarchy for Polynomial Optimization on the Hypercube
by Klerk, Etienne and Laurent, Monique
Mathematics of Operations Research, ISSN 0364-765X, 2/2020, Volume 45, Issue 1, pp. 86 - 98
We study the convergence rate of a hierarchy of upper bounds for polynomial optimization problems, proposed by Lasserre, and a related hierarchy by de Klerk,... 
Jacobi polynomials | Primary: programming: nonlinear (theory) | 90C30 | 90C22 | extremal roots of orthogonal polynomials | polynomial optimization | Lasserre hierarchy | 90C26 | semidefinite optimization
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12. Full Text On the relation between MPECs and optimization problems in abs-normal form
by Hegerhorst-Schultchen, L.C and Kirches, C and Steinbach, M.C
Optimization Methods and Software, ISSN 1055-6788, 2019, pp. 1 - 16
MPECs | stationarity conditions | 90C30 | abs-normal form | 90C46 | 90C33 | constraint qualifications | Non-smooth optimization
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13. Full Text A game-theoretic approach to computation offloading in mobile cloud computing
by Cardellini, Valeria and Cardellini, Valeria and De Nitto Personé, Vittoria and De Nitto Personé, Vittoria and Di Valerio, Valerio and Di Valerio, Valerio and Facchinei, Francisco and Facchinei, Francisco and Grassi, Vincenzo and Grassi, Vincenzo and Lo Presti, Francesco and Lo Presti, Francesco and Piccialli, Veronica and Piccialli, Veronica
Mathematical Programming, ISSN 0025-5610, 6/2016, Volume 157, Issue 2, pp. 421 - 449
We consider a three-tier architecture for mobile and pervasive computing scenarios, consisting of a local tier of mobile nodes, a middle tier (cloudlets) of... 
Theoretical, Mathematical and Computational Physics | Mobile cloud computing | Mathematics | Generalized Nash equilibrium problem | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Distributed algorithm | 68M20 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | Computer science | Cloud computing | Algorithms | Game theory | Analysis | Studies | Wireless communications | Mathematical analysis | Ubiquitous computing | Architecture (computers) | Servers | Mobile computing | Constraining | Mathematical programming
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14. Full Text A coordinate gradient descent method for nonsmooth separable minimization
by Tseng, Paul and Tseng, Paul and Yun, Sangwoon and Yun, Sangwoon
Mathematical Programming, ISSN 0025-5610, 3/2009, Volume 117, Issue 1, pp. 387 - 423
We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained... 
Global convergence | 65K05 | Mathematical and Computational Physics | 90C06 | Error bound | Mathematics | 90C26 | Coordinate descent | Linear convergence rate | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | 90C55 | Nonsmooth optimization | 49M27 | 49M37 | Combinatorics | REGRESSION | MATHEMATICS, APPLIED | error bound | CONTINUOUSLY DIFFERENTIABLE FUNCTION | linear convergence rate | ASCENT METHODS | global convergence | ALGORITHM | coordinate descent | nonsmooth optimization | LINEAR CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONDIFFERENTIABLE OPTIMIZATION PROBLEMS | CONSTRAINTS | UNCONSTRAINED OPTIMIZATION | WAVELET SHRINKAGE | CONVEX MINIMIZATION | Studies | Optimization | Mathematical programming
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15. Full Text Perturbation of error bounds
by Kruger, A Y and Kruger, A Y and López, M A and López, M A and Théra, M A and Théra, M A
Mathematical Programming, ISSN 0025-5610, 3/2018, Volume 168, Issue 1, pp. 533 - 554
Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280–3296, 2010. doi:10.1137/100782206) and, more precisely,... 
Metric subregularity | Theoretical, Mathematical and Computational Physics | Subdifferential | Error bound | Mathematics | Perturbation | Mathematical Methods in Physics | 90C30 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Metric regularity | Combinatorics | Feasibility problem | LOWER SEMICONTINUOUS FUNCTIONS | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | SUBDIFFERENTIAL CALCULUS | SUFFICIENT CONDITIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | HOLDER METRIC SUBREGULARITY | GENERALIZED EQUATIONS | CONSTRAINT SYSTEMS | LINEAR INEQUALITIES | CONVERGENCE RATE | PROJECTION ALGORITHMS | Analysis | Management science | Banach space | Error analysis | Mathematics - Optimization and Control
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16. Full Text Alternating direction augmented Lagrangian methods for semidefinite programming
by Wen, Zaiwen and Goldfarb, Donald and Yin, Wotao
Mathematical Programming Computation, ISSN 1867-2949, 12/2010, Volume 2, Issue 3, pp. 203 - 230
We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration,... 
Alternating direction method | Augmented Lagrangian method | Semidefinite programming | 90C30 | 90C35 | Operations Research/Decision Theory | 90C22 | 90C06 | Mathematics | Optimization
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17. Full Text Nonsmooth optimization via quasi-Newton methods
by Lewis, Adrian S and Lewis, Adrian S and Overton, Michael L and Overton, Michael L
Mathematical Programming, ISSN 0025-5610, 10/2013, Volume 141, Issue 1, pp. 135 - 163
We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f, not necessarily convex. We introduce an inexact line search... 
65K05 | Theoretical, Mathematical and Computational Physics | Partly smooth | Mathematics | BFGS | Line search | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Clarke stationary | R-linear convergence | Combinatorics | Nonconvex | VARIABLE-METRIC METHOD | MATHEMATICS, APPLIED | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BFGS METHOD | GLOBAL CONVERGENCE | Management science | Algorithms | Analysis | Methods | Studies | Functions (mathematics) | Sequences | Searching | Mathematical analysis | Norms | Mathematical models | Dynamical systems | Convergence
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18. Full Text Computing Maximal Copies of Polyhedra Contained in a Polyhedron
by Firsching, Moritz
Experimental Mathematics, ISSN 1058-6458, 01/2015, Volume 24, Issue 1, pp. 98 - 105
Kepler (1619) and Croft (1980) considered the problem of finding the largest homothetic copies of one regular polyhedron contained in another regular... 
polytopes | 90C30 | 51M20 | 52C17 | nonlinear optimization | MATHEMATICS
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