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

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

Journal Article

Numerical algorithms, ISSN 1572-9265, 2015, Volume 72, Issue 4, pp. 835 - 864

The purpose of this paper is to study split feasibility problems and fixed point problems concerning left Bregman strongly relatively nonexpansive mappings in...

Strong convergence | Uniformly smooth | Numeric Computing | Theory of Computation | Left Bregman strongly nonexpansive mappings | Split feasibility problem | Fixed point problem | Algorithms | Algebra | 49J53 | 90C25 | Numerical Analysis | Computer Science | 65K10 | 49M37 | Uniformly convex | PROJECTION | MATHEMATICS, APPLIED | NONEXPANSIVE OPERATORS | THEOREMS | SETS | CQ ALGORITHM

Strong convergence | Uniformly smooth | Numeric Computing | Theory of Computation | Left Bregman strongly nonexpansive mappings | Split feasibility problem | Fixed point problem | Algorithms | Algebra | 49J53 | 90C25 | Numerical Analysis | Computer Science | 65K10 | 49M37 | Uniformly convex | PROJECTION | MATHEMATICS, APPLIED | NONEXPANSIVE OPERATORS | THEOREMS | SETS | CQ ALGORITHM

Journal Article

Journal of Elasticity, ISSN 0374-3535, 4/2017, Volume 127, Issue 2, pp. 151 - 178

We study a new class of elliptic variational-hemivariational inequalities in reflexive Banach spaces. An inequality in the class is governed by a nonlinear...

Penalty operator | Classical Mechanics | Frictional contact | 74M15 | Continuous dependence | Physics | 74M10 | 47J22 | Clarke subdifferential | 47J20 | 49J53 | Automotive Engineering | Variational-hemivariational inequality | Existence and uniqueness | EXISTENCE | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | OPERATORS | Computer science | Analysis | Foundations | Uniqueness | Inequalities | Mathematical models | Banach space | Displacement | Convergence | Contact | Mathematics

Penalty operator | Classical Mechanics | Frictional contact | 74M15 | Continuous dependence | Physics | 74M10 | 47J22 | Clarke subdifferential | 47J20 | 49J53 | Automotive Engineering | Variational-hemivariational inequality | Existence and uniqueness | EXISTENCE | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | OPERATORS | Computer science | Analysis | Foundations | Uniqueness | Inequalities | Mathematical models | Banach space | Displacement | Convergence | Contact | Mathematics

Journal Article

Advances in nonlinear analysis, ISSN 2191-950X, 2018, Volume 7, Issue 4, pp. 571 - 586

The aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution...

35R70 | Partial differential hemivariational inequality | 49J53 | properties of the solution set | well-posedness | Hausdorff MNC | semigroup | VARIATIONAL-INEQUALITIES | MATHEMATICS | MATHEMATICS, APPLIED | C-0-semigroup | FINITE-DIMENSIONAL SPACES | CONVERGENCE | LINEAR COMPLEMENTARITY SYSTEMS | Mathematics

35R70 | Partial differential hemivariational inequality | 49J53 | properties of the solution set | well-posedness | Hausdorff MNC | semigroup | VARIATIONAL-INEQUALITIES | MATHEMATICS | MATHEMATICS, APPLIED | C-0-semigroup | FINITE-DIMENSIONAL SPACES | CONVERGENCE | LINEAR COMPLEMENTARITY SYSTEMS | Mathematics

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 9/2019, Volume 27, Issue 3, pp. 643 - 664

We introduce, in a natural way, a new notion of asymptotic map for a set-valued map. The non-uniqueness of such an asymptotic map leads to consider equivalent...

49J53 | Analysis | 65K10 | Mathematics | Asymptotic analysis | Set-valued map | Set optimization problem | 54C60 | Optimization | MATHEMATICS, APPLIED | EXISTENCE THEOREMS

49J53 | Analysis | 65K10 | Mathematics | Asymptotic analysis | Set-valued map | Set optimization problem | 54C60 | Optimization | MATHEMATICS, APPLIED | EXISTENCE THEOREMS

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 3/2019, Volume 27, Issue 1, pp. 265 - 294

We provide a precise characterization of the weak sequential closure of nonempty, closed, decomposable sets in Lebesgue spaces. Therefore, we have to...

Measurability | Weak sequential closure | 90C30 | 49J53 | Limiting normal cone | Analysis | Lebesgue spaces | Mathematics | 28B05 | Decomposable set | Optimization | INTEGRALS | MATHEMATICS, APPLIED | Computer science

Measurability | Weak sequential closure | 90C30 | 49J53 | Limiting normal cone | Analysis | Lebesgue spaces | Mathematics | 28B05 | Decomposable set | Optimization | INTEGRALS | MATHEMATICS, APPLIED | Computer science

Journal Article

Journal of global optimization, ISSN 1573-2916, 2018, Volume 73, Issue 3, pp. 567 - 581

In this paper, we supply the power set $${\mathcal {P}}(Z)$$ P ( Z ) of a partially ordered normed space Z with a transitive and irreflexive binary relation...

54A20 | 49J53 | Set-valued optimization | Operations Research/Decision Theory | 65K10 | Mathematics | Set approach | Strict ordering | Computer Science, general | Optimization | Real Functions | Set convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZERS | Topology | Convergence | Optimization and Control

54A20 | 49J53 | Set-valued optimization | Operations Research/Decision Theory | 65K10 | Mathematics | Set approach | Strict ordering | Computer Science, general | Optimization | Real Functions | Set convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZERS | Topology | Convergence | Optimization and Control

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 12/2019, Volume 27, Issue 4, pp. 921 - 947

We study the invertibility nonsmooth maps between infinite-dimensional Banach spaces. To this end, we introduce an analogue of the notion of pseudo-Jacobian...

Pseudo-Jacobian | Hadamard integral condition | Nonsmooth analysis | 49J53 | 49J52 | Analysis | Global invertibility | Mathematics | 46G05 | Optimization

Pseudo-Jacobian | Hadamard integral condition | Nonsmooth analysis | 49J53 | 49J52 | Analysis | Global invertibility | Mathematics | 46G05 | Optimization

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 2019, Volume 27, Issue 4, pp. 995 - 1023

Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates...

90C31 | Semi-infinite programming | Hölder error bounds | 49J53 | 90C25 | Analysis | 90C34 | Mathematics | Convex programming | Optimization | Hölder calmness

90C31 | Semi-infinite programming | Hölder error bounds | 49J53 | 90C25 | Analysis | 90C34 | Mathematics | Convex programming | Optimization | Hölder calmness

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 16

In this paper, we study the split DC program by using the split proximal linearized algorithm. Further, linear convergence theorem for the proposed algorithm...

Proximal linearized algorithm | 49M30 | 49J53 | Analysis | 49J50 | Mathematics, general | Mathematics | 90C26 | Applications of Mathematics | 49M37 | DC program | Strongly monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENCE | DUALITY | Theorems | Algorithms | Linearization | Convergence

Proximal linearized algorithm | 49M30 | 49J53 | Analysis | 49J50 | Mathematics, general | Mathematics | 90C26 | Applications of Mathematics | 49M37 | DC program | Strongly monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENCE | DUALITY | Theorems | Algorithms | Linearization | Convergence

Journal Article

11.
Full Text
Critical multipliers in variational systems via second-order generalized differentiation

Mathematical Programming, ISSN 0025-5610, 6/2018, Volume 169, Issue 2, pp. 605 - 648

In this paper we introduce the notions of critical and noncritical multipliers for variational systems and extend to a general framework the corresponding...

Theoretical, Mathematical and Computational Physics | Composite optimization | Mathematics | Lipschitzian stability | Critical and noncritical multipliers | Variational systems | 90C31 | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Combinatorics | Robust isolated calmness | Generalized differentiation | Piecewise linear functions | MATHEMATICS, APPLIED | CALMNESS | EQUATIONS | TILT STABILITY | LIPSCHITZIAN | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSTRAINT SYSTEMS | OPTIMIZATION | COMPUTATION | 1ST-ORDER | DERIVATIVES | FULL STABILITY | Algorithms | Economic models | Minimax technique | Maps | Multipliers | Robustness (mathematics) | Equivalence | Optimization

Theoretical, Mathematical and Computational Physics | Composite optimization | Mathematics | Lipschitzian stability | Critical and noncritical multipliers | Variational systems | 90C31 | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Combinatorics | Robust isolated calmness | Generalized differentiation | Piecewise linear functions | MATHEMATICS, APPLIED | CALMNESS | EQUATIONS | TILT STABILITY | LIPSCHITZIAN | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSTRAINT SYSTEMS | OPTIMIZATION | COMPUTATION | 1ST-ORDER | DERIVATIVES | FULL STABILITY | Algorithms | Economic models | Minimax technique | Maps | Multipliers | Robustness (mathematics) | Equivalence | Optimization

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2017, Volume 177, Issue 3, pp. 679 - 695

Hern$$\acute{\mathrm{a}}$$ a´ ndez and Rodríguez-Marín (J Math Anal Appl 325:1–18, 2007) introduced a nonlinear scalarizing function for sets, which is a...

90C29 | Mathematics | Theory of Computation | Optimization | Nonlinear scalarizing function | 49J53 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Continuity | Applications of Mathematics | Engineering, general | Convexity | Set optimization problem | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILITY | VECTOR EQUILIBRIUM PROBLEMS | VALUED MAPS | MAPPINGS | WELL-POSEDNESS | Economic models | Continuity (mathematics)

90C29 | Mathematics | Theory of Computation | Optimization | Nonlinear scalarizing function | 49J53 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Continuity | Applications of Mathematics | Engineering, general | Convexity | Set optimization problem | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILITY | VECTOR EQUILIBRIUM PROBLEMS | VALUED MAPS | MAPPINGS | WELL-POSEDNESS | Economic models | Continuity (mathematics)

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 2018, Volume 27, Issue 3, pp. 665 - 692

The theory of subdifferentials provides adequate methods and tools to put descent methods for nonsmooth optimization problems into practice. However, in...

Subdifferentials | 49J53 | Set-valued mapping | 49J52 | Analysis | Descent method | Mathematics | Nonsmooth optimization | 90C26 | Optimization | MATHEMATICS, APPLIED | CALCULUS

Subdifferentials | 49J53 | Set-valued mapping | 49J52 | Analysis | Descent method | Mathematics | Nonsmooth optimization | 90C26 | Optimization | MATHEMATICS, APPLIED | CALCULUS

Journal Article

Mathematical programming, ISSN 1436-4646, 2018, Volume 174, Issue 1-2, pp. 167 - 194

Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth. This fact motivates...

Theoretical, Mathematical and Computational Physics | Mathematics | 90C15 | Probabilistic constraint | Probability functions | Mathematical Methods in Physics | Clarke subdifferential | 90C30 | Mordukhovich subdifferential | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Spheric-radial decomposition | Combinatorics | Stochastic optimization | Multivariate Gaussian distribution | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Gaussian processes | Gaussian distribution | Statistical analysis | Normal distribution | Continuity (mathematics)

Theoretical, Mathematical and Computational Physics | Mathematics | 90C15 | Probabilistic constraint | Probability functions | Mathematical Methods in Physics | Clarke subdifferential | 90C30 | Mordukhovich subdifferential | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Spheric-radial decomposition | Combinatorics | Stochastic optimization | Multivariate Gaussian distribution | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Gaussian processes | Gaussian distribution | Statistical analysis | Normal distribution | Continuity (mathematics)

Journal Article

Set-valued and variational analysis, ISSN 1877-0533, 2012, Volume 21, Issue 2, pp. 151 - 176

This paper mainly deals with the study of directional versions of metric regularity and metric subregularity for general set-valued mappings between...

Geometry | Subregularity | 49J53 | Analysis | Mathematics | 90C48 | Metric regularity | M-stationarity | 49K27 | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | CALMNESS | INCLUSIONS | SUFFICIENT CONDITIONS | THEOREM | STABILITY | CONSTRAINT QUALIFICATIONS | GENERALIZED EQUATIONS | MAPPINGS | SYSTEMS

Geometry | Subregularity | 49J53 | Analysis | Mathematics | 90C48 | Metric regularity | M-stationarity | 49K27 | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | CALMNESS | INCLUSIONS | SUFFICIENT CONDITIONS | THEOREM | STABILITY | CONSTRAINT QUALIFICATIONS | GENERALIZED EQUATIONS | MAPPINGS | SYSTEMS

Journal Article

Optimization Letters, ISSN 1862-4472, 10/2014, Volume 8, Issue 7, pp. 2099 - 2110

In this paper our interest is in investigating properties and numerical solutions of Proximal Split feasibility Problems. First, we consider the problem of...

Computational Intelligence | 49J53 | 90C25 | Operations Research/Decision Theory | Numerical and Computational Physics | 65K10 | Mathematics | 49M37 | Moreau–Yosida approximate | Optimization | Proximal split feasibility problems | Prox-regularity | Moreau-Yosida approximate | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SET | CONVEX | REGULAR FUNCTIONS | Algorithms

Computational Intelligence | 49J53 | 90C25 | Operations Research/Decision Theory | Numerical and Computational Physics | 65K10 | Mathematics | 49M37 | Moreau–Yosida approximate | Optimization | Proximal split feasibility problems | Prox-regularity | Moreau-Yosida approximate | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SET | CONVEX | REGULAR FUNCTIONS | Algorithms

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2019, Volume 180, Issue 1, pp. 1 - 4

This is the Preface to the Special Issue of JOTA dedicated to the 60th birthday of Professor Aram V. Arutyunov

Mathematics | Theory of Computation | Optimization | 90C20 | 47H10 | 49J20 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Applications of Mathematics | Engineering, general | Nonlinear and variational analysis | 49J15 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Nonlinear analysis

Mathematics | Theory of Computation | Optimization | 90C20 | 47H10 | 49J20 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Applications of Mathematics | Engineering, general | Nonlinear and variational analysis | 49J15 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Nonlinear analysis

Journal Article

Mathematical programming, ISSN 1436-4646, 2014, Volume 153, Issue 2, pp. 333 - 362

In this paper we derive new fractional error bounds for polynomial systems with exponents explicitly determined by the dimension of the underlying space and...

Variational analysis | Łojasiewicz’s inequality | Polynomial optimization and complementarity | 26D10 | Theoretical, Mathematical and Computational Physics | Hölderian stability | Mathematics | 90C26 | 90C31 | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Error bounds | Polynomials | Combinatorics | Generalized differentiation | LOJASIEWICZ EXPONENT | MATHEMATICS, APPLIED | WEAK SHARP MINIMA | INEQUALITY | Holderian stability | TILT STABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONSMOOTH | Lojasiewicz's inequality | LINEAR REGULARITY | Studies | Optimization | Mathematical programming | Errors | Tensors | Stability | Exponents | Mathematical analysis | Eigenvalues

Variational analysis | Łojasiewicz’s inequality | Polynomial optimization and complementarity | 26D10 | Theoretical, Mathematical and Computational Physics | Hölderian stability | Mathematics | 90C26 | 90C31 | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Error bounds | Polynomials | Combinatorics | Generalized differentiation | LOJASIEWICZ EXPONENT | MATHEMATICS, APPLIED | WEAK SHARP MINIMA | INEQUALITY | Holderian stability | TILT STABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONSMOOTH | Lojasiewicz's inequality | LINEAR REGULARITY | Studies | Optimization | Mathematical programming | Errors | Tensors | Stability | Exponents | Mathematical analysis | Eigenvalues

Journal Article