Numerische Mathematik, ISSN 0029-599X, 02/2018, Volume 138, Issue 2, pp. 273 - 299

Journal Article

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

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

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 10/2017, Volume 96, Issue 2, pp. 455 - 481

A curve θ:I→E in a metric space E equipped with the distance d, where I⊂R is a (possibly unbounded) interval, is called self‐contracted, if for any triple of...

53A04 | 49J53 | 49J52 | 52A21 (primary) | 37N40 | 65K10 (secondary) | MATHEMATICS

53A04 | 49J53 | 49J52 | 52A21 (primary) | 37N40 | 65K10 (secondary) | MATHEMATICS

Journal Article

Inverse Problems in Science and Engineering, ISSN 1741-5977, 2018, pp. 1 - 11

Journal Article

Communications in Mathematical Sciences, ISSN 1539-6746, 2010, Volume 8, Issue 1, pp. 93 - 111

We propose and analyze an extremely fast, efficient, and simple method for solving the problem: min{parallel to u parallel to(1) : Au = f, u is an element of...

Basis pursuit | minimization | Compressed sensing | Sparse denoising | Iterative regularization | MATHEMATICS, APPLIED | sparse denoising | compressed sensing | l-minimization | basis pursuit | iterative regularization | ℓ^1-minimization | 90-08 | 65K10 | 49M99

Basis pursuit | minimization | Compressed sensing | Sparse denoising | Iterative regularization | MATHEMATICS, APPLIED | sparse denoising | compressed sensing | l-minimization | basis pursuit | iterative regularization | ℓ^1-minimization | 90-08 | 65K10 | 49M99

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2016, Volume 159, Issue 1, pp. 253 - 287

We revisit the proofs of convergence for a first order primal–dual algorithm for convex optimization which we have studied a few years ago. In particular, we...

Theoretical, Mathematical and Computational Physics | Convergence rates | Ergodic convergence | Mathematics | 65Y20 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 49M29 | First order algorithms | 65K10 | Combinatorics | Saddle-point problems | Primal–dual algorithms | BREGMAN FUNCTIONS | MATHEMATICS, APPLIED | Primal-dual algorithms | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | INCLUSIONS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MAPPINGS | Graphics software | Algorithms | Studies | Mathematical analysis | Mathematical programming | Computational geometry | Operators | Proving | Norms | Nonlinearity | Optimization | Convergence

Theoretical, Mathematical and Computational Physics | Convergence rates | Ergodic convergence | Mathematics | 65Y20 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 49M29 | First order algorithms | 65K10 | Combinatorics | Saddle-point problems | Primal–dual algorithms | BREGMAN FUNCTIONS | MATHEMATICS, APPLIED | Primal-dual algorithms | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | INCLUSIONS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MAPPINGS | Graphics software | Algorithms | Studies | Mathematical analysis | Mathematical programming | Computational geometry | Operators | Proving | Norms | Nonlinearity | Optimization | Convergence

Journal Article

Journal of the Australian Mathematical Society, ISSN 1446-7887, 2019, pp. 1 - 23

As a continuation of previous work of the first author with Ranjbar [‘A variational inequality in complete CAT(0) spaces’, J. Fixed Point Theory Appl. 17...

secondary 90C25 | 47J20 | primary 47H05 | 49J40 | 2010 Mathematics subject classification | 65K10 | 47J25

secondary 90C25 | 47J20 | primary 47H05 | 49J40 | 2010 Mathematics subject classification | 65K10 | 47J25

Journal Article

Mathematical intelligencer, ISSN 0343-6993, 04/2015, Volume 38

Each metro line usually has its own color on the map. For obvious reasons, these colors should be maximally different. Suppose a new metro line is built. We...

00A66, 65K10, 37C10, 37C50 | math.OC | math.MG

00A66, 65K10, 37C10, 37C50 | math.OC | math.MG

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 12/2017, Volume 25, Issue 4, pp. 701 - 729

We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary...

Metric subregularity | 65K05 | Normal cone | Probability Theory and Stochastic Processes | Error bound | Mathematics | Transversality | Alternating projections | Linear convergence | Secondary 49K40 | 90C30 | Intrinsic transversality | Analysis | 65K10 | 49M05 | Metric regularity | 49M37 | Primary 49J53 | Subtransversality | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | WEAK SHARP MINIMA | CONVEX-SETS | ALGORITHMS | STRONG CHIP | CONVERGENCE | ERROR-BOUNDS | LINEAR REGULARITY | Mathematics - Optimization and Control

Metric subregularity | 65K05 | Normal cone | Probability Theory and Stochastic Processes | Error bound | Mathematics | Transversality | Alternating projections | Linear convergence | Secondary 49K40 | 90C30 | Intrinsic transversality | Analysis | 65K10 | 49M05 | Metric regularity | 49M37 | Primary 49J53 | Subtransversality | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | WEAK SHARP MINIMA | CONVEX-SETS | ALGORITHMS | STRONG CHIP | CONVERGENCE | ERROR-BOUNDS | LINEAR REGULARITY | Mathematics - Optimization and Control

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2016, Volume 171, Issue 2, pp. 600 - 616

We investigate the convergence of a forward–backward–forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth...

Inertial proximal algorithm | Limiting subdifferential | Mathematics | Theory of Computation | 90C26 | Bregman distance | Tseng’s type proximal algorithm | Optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | 65K10 | Nonsmooth optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Kurdyka–Łojasiewicz inequality

Inertial proximal algorithm | Limiting subdifferential | Mathematics | Theory of Computation | 90C26 | Bregman distance | Tseng’s type proximal algorithm | Optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | 65K10 | Nonsmooth optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Kurdyka–Łojasiewicz inequality

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 12/2017, Volume 68, Issue 3, pp. 719 - 747

Markov–Dubins path is the shortest planar curve joining two points with prescribed tangents, with a specified bound on its curvature. Its structure, as proved...

Secondary 65K10 | Mathematics | Bang–bang control | Statistics, general | Bounded curvature | Optimization | Singular control | Primary 49J15 | 90C30 | Abnormal optimal control problem | Operations Research/Decision Theory | Convex and Discrete Geometry | Optimal control | Operations Research, Management Science | Markov–Dubins path | 49K15 | MATHEMATICS, APPLIED | SEARCH | INEXACT RESTORATION | 2ND-ORDER SUFFICIENT CONDITIONS | ALGORITHM | CURVES | ACCELERATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Bang-bang control | EULER DISCRETIZATION | CURVATURE | OPTIMIZATION | Markov-Dubins path | SURFACES | Tangents | Numerical analysis | Markov processes | Maximum principle | Control theory | Curvature | Mathematics - Optimization and Control

Secondary 65K10 | Mathematics | Bang–bang control | Statistics, general | Bounded curvature | Optimization | Singular control | Primary 49J15 | 90C30 | Abnormal optimal control problem | Operations Research/Decision Theory | Convex and Discrete Geometry | Optimal control | Operations Research, Management Science | Markov–Dubins path | 49K15 | MATHEMATICS, APPLIED | SEARCH | INEXACT RESTORATION | 2ND-ORDER SUFFICIENT CONDITIONS | ALGORITHM | CURVES | ACCELERATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Bang-bang control | EULER DISCRETIZATION | CURVATURE | OPTIMIZATION | Markov-Dubins path | SURFACES | Tangents | Numerical analysis | Markov processes | Maximum principle | Control theory | Curvature | Mathematics - Optimization and Control

Journal Article

Numerische Mathematik, ISSN 0029-599X, 05/2016, Volume 133, Issue 1, pp. 67 - 102

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes...

35J20 | 65K10 | 65C30 | 60H15 | 49N10 | MATHEMATICS, APPLIED | OPTIMIZATION | COLLOCATION METHOD | APPROXIMATION | PARTIAL-DIFFERENTIAL-EQUATIONS | EMPIRICAL INTERPOLATION METHOD | Algorithms | Anisotropy | Analysis | Methods

35J20 | 65K10 | 65C30 | 60H15 | 49N10 | MATHEMATICS, APPLIED | OPTIMIZATION | COLLOCATION METHOD | APPROXIMATION | PARTIAL-DIFFERENTIAL-EQUATIONS | EMPIRICAL INTERPOLATION METHOD | Algorithms | Anisotropy | Analysis | Methods

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2016, Volume 170, Issue 1, pp. 72 - 84

Recently, the tensor complementarity problem has been investigated in the literature. An important question involving the property of global uniqueness and...

Tensor complementarity problem | Mathematics | Theory of Computation | 15A69 | Optimization | Strong P tensor | 15A18 | P tensor | 65F10 | Calculus of Variations and Optimal Control; Optimization | 90C33 | 65K10 | 65F15 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Nonlinear complementarity problem | Global uniqueness and solvability | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | POSITIVE-DEFINITE | Studies | Mathematical analysis | Nonlinear systems | Construction | Tensors | Uniqueness

Tensor complementarity problem | Mathematics | Theory of Computation | 15A69 | Optimization | Strong P tensor | 15A18 | P tensor | 65F10 | Calculus of Variations and Optimal Control; Optimization | 90C33 | 65K10 | 65F15 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Nonlinear complementarity problem | Global uniqueness and solvability | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | POSITIVE-DEFINITE | Studies | Mathematical analysis | Nonlinear systems | Construction | Tensors | Uniqueness

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 12/2019, Volume 81, Issue 3, pp. 1240 - 1265

This paper develops and analyzes a new numerical scheme for solving hyperbolic conservation laws that combines the Lax Wendroff method with $$l_1$$ l 1...

Conservation laws | 65M15 | Computational Mathematics and Numerical Analysis | Algorithms | 65M08 | l_1$$ l 1 regularization | Polynomial annihilation | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 65K10 | Mathematics

Conservation laws | 65M15 | Computational Mathematics and Numerical Analysis | Algorithms | 65M08 | l_1$$ l 1 regularization | Polynomial annihilation | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 65K10 | Mathematics

Journal Article

Optimization, ISSN 0233-1934, 02/2017, Volume 66, Issue 2, pp. 205 - 224

We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and...

optimization problem | Idempotent semifield | scheduling objective | 65K05 | project scheduling | 90B35 | 65K10 | 90C48 | precedence relationship | 15A80 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LINEAR CONSTRAINTS | Project management | Production scheduling | Optimization | Finishes | Mathematical analysis | Mathematical models | Scheduling | Vectors (mathematics) | Deviation | Due dates

optimization problem | Idempotent semifield | scheduling objective | 65K05 | project scheduling | 90B35 | 65K10 | 90C48 | precedence relationship | 15A80 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LINEAR CONSTRAINTS | Project management | Production scheduling | Optimization | Finishes | Mathematical analysis | Mathematical models | Scheduling | Vectors (mathematics) | Deviation | Due dates

Journal Article

Optimization Methods and Software, ISSN 1055-6788, 2018, pp. 1 - 21

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 02/2018, Volume 125, Issue 2, pp. 158 - 163

The Cauchy radius of a polynomial is a classical upper bound from 1829 on the magnitude of the largest zero of a polynomial, which was improved in 2002 by...

Secondary 30C15; 65H04; 65K10 | Primary 12D10 | MATHEMATICS

Secondary 30C15; 65H04; 65K10 | Primary 12D10 | MATHEMATICS

Journal Article

18.
Full Text
Variational phase recovering without phase unwrapping in phase-shifting interferometry

International Journal of Computer Mathematics, ISSN 0020-7160, 06/2019, Volume 96, Issue 6, pp. 1217 - 1229

We present a variational method for recovering the phase term from the information obtained from phase-shifting methods. First we introduce the new method...

78A99 | 68U10 | 65F22 | phase retrieval | 65K10 | Fringe analysis | image reconstruction techniques | 65N22 | MATHEMATICS, APPLIED | NOISE REMOVAL | Algorithms

78A99 | 68U10 | 65F22 | phase retrieval | 65K10 | Fringe analysis | image reconstruction techniques | 65N22 | MATHEMATICS, APPLIED | NOISE REMOVAL | Algorithms

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 07/2019

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 11/2018, Volume 18, Issue 4, pp. 649 - 669

Journal Article

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