Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2015, Volume 167, Issue 2, pp. 502 - 526

In this paper, we derive exact chain rules for a proper epsilon-subdifferential in the sense of Benson of extended vector mappings, recently introduced by...

Proper $$\varepsilon $$ ε -efficiency | 90C29 | Mathematics | Theory of Computation | 90C48 | Strong $$\varepsilon $$ ε -efficiency | Optimization | Strong $$\varepsilon $$ ε -subdifferential | Proper $$\varepsilon $$ ε -subdifferential | Calculus of Variations and Optimal Control; Optimization | 90C25 | 49J52 | Nearly cone-subconvexlikeness | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Linear scalarization | 49K27 | Vector optimization

Proper $$\varepsilon $$ ε -efficiency | 90C29 | Mathematics | Theory of Computation | 90C48 | Strong $$\varepsilon $$ ε -efficiency | Optimization | Strong $$\varepsilon $$ ε -subdifferential | Proper $$\varepsilon $$ ε -subdifferential | Calculus of Variations and Optimal Control; Optimization | 90C25 | 49J52 | Nearly cone-subconvexlikeness | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Linear scalarization | 49K27 | Vector optimization

Journal Article

Set-Valued and Variational Analysis, ISSN 0927-6947, 06/2017, Volume 25, Issue 2, pp. 383 - 403

In this paper, several sequential formulae are obtained for the Brondsted-Rockafellar epsilon-subdifferential of the sum and the composition of two convex and...

ε-subdifferential | Benson (C,ε)-proper subdifferential | p-regularly ε-subdifferentiable vector mapping | Sequential ε-subdifferential calculus | q-strong subdifferential | Brøndsted-Rockafellar theorem | epsilon-subdifferential | MATHEMATICS, APPLIED | Brondsted-Rockafellar theorem | CONVEX-FUNCTIONS | QUALIFICATION | p-regularly epsilon-subdifferentiable vector mapping | BANACH-SPACES | PROPER APPROXIMATE SOLUTIONS | Sequential epsilon-subdifferential calculus | OPTIMIZATION | Benson (C, epsilon)-proper subdifferential | OPTIMALITY | Mathematics

ε-subdifferential | Benson (C,ε)-proper subdifferential | p-regularly ε-subdifferentiable vector mapping | Sequential ε-subdifferential calculus | q-strong subdifferential | Brøndsted-Rockafellar theorem | epsilon-subdifferential | MATHEMATICS, APPLIED | Brondsted-Rockafellar theorem | CONVEX-FUNCTIONS | QUALIFICATION | p-regularly epsilon-subdifferentiable vector mapping | BANACH-SPACES | PROPER APPROXIMATE SOLUTIONS | Sequential epsilon-subdifferential calculus | OPTIMIZATION | Benson (C, epsilon)-proper subdifferential | OPTIMALITY | Mathematics

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2015, Volume 167, Issue 2, pp. 502 - 526

In this paper, we derive exact chain rules for a proper epsilon-subdifferential in the sense of Benson of extended vector mappings, recently introduced by...

Proper ε-subdifferential | Strong ε-efficiency | Nearly cone-subconvexlikeness | Proper ε-efficiency | Strong ε-subdifferential | Linear scalarization | Vector optimization | Proper epsilon-efficiency | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | Proper epsilon-subdifferential | Strong epsilon-subdifferential | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMALITY CONDITIONS | POINTS | Strong epsilon-efficiency | Mathematics

Proper ε-subdifferential | Strong ε-efficiency | Nearly cone-subconvexlikeness | Proper ε-efficiency | Strong ε-subdifferential | Linear scalarization | Vector optimization | Proper epsilon-efficiency | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | Proper epsilon-subdifferential | Strong epsilon-subdifferential | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMALITY CONDITIONS | POINTS | Strong epsilon-efficiency | Mathematics

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 2/2019, Volume 180, Issue 2, pp. 397 - 427

This paper aims at providing some formulae for the subdifferential and the conjungate function of the supremum function over an arbitrary family of functions....

Pointwise supremum function | Mathematics | Theory of Computation | Optimization | Calculus of Variations and Optimal Control; Optimization | varepsilon $$ ε -Subdifferential | 90C25 | Operations Research/Decision Theory | 90C34 | Applications of Mathematics | Engineering, general | Fenchel conjugate | 46N10 | Convex analysis | ε-Subdifferential | MATHEMATICS, APPLIED | SET | CALCULUS RULES | FENCHEL SUBDIFFERENTIALS | EPSILON-SUBDIFFERENTIALS | EPI-POINTED FUNCTIONS | MINIMAX | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | epsilon-Subdifferential | INTEGRATION | CONVEX | PROPER APPROXIMATE SOLUTIONS | Employee motivation | Analysis

Pointwise supremum function | Mathematics | Theory of Computation | Optimization | Calculus of Variations and Optimal Control; Optimization | varepsilon $$ ε -Subdifferential | 90C25 | Operations Research/Decision Theory | 90C34 | Applications of Mathematics | Engineering, general | Fenchel conjugate | 46N10 | Convex analysis | ε-Subdifferential | MATHEMATICS, APPLIED | SET | CALCULUS RULES | FENCHEL SUBDIFFERENTIALS | EPSILON-SUBDIFFERENTIALS | EPI-POINTED FUNCTIONS | MINIMAX | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | epsilon-Subdifferential | INTEGRATION | CONVEX | PROPER APPROXIMATE SOLUTIONS | Employee motivation | Analysis

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 03/2013, Volume 79, Issue 1, pp. 52 - 67

The aim of this work is to introduce a proper -subdifferential in the sense of Benson for extended mappings between topological linear spaces. It is defined by...

Proper [formula omitted]-subdifferential | Linear scalarization | Proper [formula omitted]-efficiency | Nearly subconvexlikeness | [formula omitted]-subdifferential | Vector optimization | ε-subdifferential | Proper ε-subdifferential | Proper ε-efficiency | Proper epsilon-efficiency | epsilon-subdifferential | MATHEMATICS, APPLIED | Proper epsilon-subdifferential | CONES | CALCULUS | MATHEMATICS | RESPECT | SCALARIZATION | OPTIMALITY CONDITIONS | POINTS | EFFICIENCY

Proper [formula omitted]-subdifferential | Linear scalarization | Proper [formula omitted]-efficiency | Nearly subconvexlikeness | [formula omitted]-subdifferential | Vector optimization | ε-subdifferential | Proper ε-subdifferential | Proper ε-efficiency | Proper epsilon-efficiency | epsilon-subdifferential | MATHEMATICS, APPLIED | Proper epsilon-subdifferential | CONES | CALCULUS | MATHEMATICS | RESPECT | SCALARIZATION | OPTIMALITY CONDITIONS | POINTS | EFFICIENCY

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 6/2019, Volume 74, Issue 2, pp. 361 - 382

In this paper, we provide variants of the Ekeland variational principle for a type of approximate proper solutions of a vector equilibrium problem, whose final...

Approximate proper solutions | Vector equilibrium problems | Ekeland variational principle | 90C29 | Mathematics | 90C26 | Optimization | 49J53 | 49J52 | Operations Research/Decision Theory | Multiobjective optimization | 90C33 | Computer Science, general | Real Functions | Variational inequalities | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Multiple objective analysis | Portfolio management | Equilibrium

Approximate proper solutions | Vector equilibrium problems | Ekeland variational principle | 90C29 | Mathematics | 90C26 | Optimization | 49J53 | 49J52 | Operations Research/Decision Theory | Multiobjective optimization | 90C33 | Computer Science, general | Real Functions | Variational inequalities | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Multiple objective analysis | Portfolio management | Equilibrium

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 4/2018, Volume 70, Issue 4, pp. 875 - 901

We deal with a constrained vector optimization problem between real linear spaces without assuming any topology and by considering an ordering defined through...

Approximate proper efficiency | Secondary 90C46 | Approximate weak efficiency | Primary 90C26 | 90C29 | Mathematics | 90C48 | algebraic interior | Optimization | Nearly E -subconvexlikeness | Lagrange multipliers | Operations Research/Decision Theory | Improvement set | Vector closure | Linear scalarization | Computer Science, general | 49K27 | Vector optimization | Real Functions | Nearly E-subconvexlikeness | MATHEMATICS, APPLIED | EPSILON-SUBDIFFERENTIALS | PROPER EFFICIENCY | WEAK | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VALUED OPTIMIZATION | MAPS | INTERIOR | SCALARIZATION | OPTIMALITY CONDITIONS | Lagrange multiplier | Vector spaces

Approximate proper efficiency | Secondary 90C46 | Approximate weak efficiency | Primary 90C26 | 90C29 | Mathematics | 90C48 | algebraic interior | Optimization | Nearly E -subconvexlikeness | Lagrange multipliers | Operations Research/Decision Theory | Improvement set | Vector closure | Linear scalarization | Computer Science, general | 49K27 | Vector optimization | Real Functions | Nearly E-subconvexlikeness | MATHEMATICS, APPLIED | EPSILON-SUBDIFFERENTIALS | PROPER EFFICIENCY | WEAK | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VALUED OPTIMIZATION | MAPS | INTERIOR | SCALARIZATION | OPTIMALITY CONDITIONS | Lagrange multiplier | Vector spaces

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 1/2016, Volume 64, Issue 1, pp. 117 - 139

In this work we introduce two approximate duality approaches for vector optimization problems. The first one by means of approximate solutions of a scalar...

Proper $$\varepsilon $$ ε -efficiency | Mathematics | 90C48 | Approximate duality | Optimization | 90C46 | 90C25 | Nearly cone-subconvexlikeness | 49N15 | Operation Research/Decision Theory | Linear scalarization | Computer Science, general | Vector optimization | Real Functions | Proper ε-efficiency | Proper epsilon-efficiency | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SADDLE-POINT THEOREMS | SCALARIZATION | SET-VALUED MAPS | EPSILON-SUBDIFFERENTIALS | EFFICIENCY | Errors | Approximation | Mathematical analysis | Texts | Scalars | Convexity | Vectors (mathematics)

Proper $$\varepsilon $$ ε -efficiency | Mathematics | 90C48 | Approximate duality | Optimization | 90C46 | 90C25 | Nearly cone-subconvexlikeness | 49N15 | Operation Research/Decision Theory | Linear scalarization | Computer Science, general | Vector optimization | Real Functions | Proper ε-efficiency | Proper epsilon-efficiency | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SADDLE-POINT THEOREMS | SCALARIZATION | SET-VALUED MAPS | EPSILON-SUBDIFFERENTIALS | EFFICIENCY | Errors | Approximation | Mathematical analysis | Texts | Scalars | Convexity | Vectors (mathematics)

Journal Article

Optimization Letters, ISSN 1862-4472, 8/2016, Volume 10, Issue 6, pp. 1287 - 1301

By using the generalized Fermat rule, the Mordukhovich subdifferential for maximum functions, the fuzzy sum rule for Fréchet subdifferentials and the sum rule...

Optimality conditions | Computational Intelligence | Multiobjective optimization | Numerical and Computational Physics | Weak sharp efficiency | Mathematics | Operation Research/Decision Theory | Mordukhovich generalized differentiation | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | LOCAL MINIMA | PROPER | MINIMIZERS

Optimality conditions | Computational Intelligence | Multiobjective optimization | Numerical and Computational Physics | Weak sharp efficiency | Mathematics | Operation Research/Decision Theory | Mordukhovich generalized differentiation | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | LOCAL MINIMA | PROPER | MINIMIZERS

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 4/2009, Volume 43, Issue 4, pp. 533 - 552

This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained problems of multiobjective...

Variational analysis | Necessary optimality conditions | 90C29 | Nonsmooth and multiobjective optimization | Super efficiency and super minimizers | Optimization | Economics / Management Science | 49J53 | 49J52 | Operations Research/Decision Theory | Computer Science, general | Generalized differentiation | Real Functions | MATHEMATICS, APPLIED | SPACES | CONES | PROPER EFFICIENCY | MAXIMIZATION | RESPECT | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | POINTS | Mathematical optimization | Analysis | Studies | Optimization techniques | Mapping | Differential equations

Variational analysis | Necessary optimality conditions | 90C29 | Nonsmooth and multiobjective optimization | Super efficiency and super minimizers | Optimization | Economics / Management Science | 49J53 | 49J52 | Operations Research/Decision Theory | Computer Science, general | Generalized differentiation | Real Functions | MATHEMATICS, APPLIED | SPACES | CONES | PROPER EFFICIENCY | MAXIMIZATION | RESPECT | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | POINTS | Mathematical optimization | Analysis | Studies | Optimization techniques | Mapping | Differential equations

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 06/2012, Volume 75, Issue 9, pp. 3761 - 3775

In this paper, first, a new notion of -strict subdifferentials of set-valued maps is introduced in a locally convex space. Second, the existence for a -strict...

Optimality conditions | [formula omitted]-strict subdifferential | Set-valued map | Near-subconvexlikeness | ε-strict subdifferential | MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | MULTIFUNCTIONS | CONES | VECTOR OPTIMIZATION PROBLEMS | MINIMIZERS | PROPER EFFICIENCY | MATHEMATICS | RESPECT | MINIMIZATION | epsilon-strict subdifferential

Optimality conditions | [formula omitted]-strict subdifferential | Set-valued map | Near-subconvexlikeness | ε-strict subdifferential | MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | MULTIFUNCTIONS | CONES | VECTOR OPTIMIZATION PROBLEMS | MINIMIZERS | PROPER EFFICIENCY | MATHEMATICS | RESPECT | MINIMIZATION | epsilon-strict subdifferential

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 72, Issue 11, pp. 3994 - 4004

In this paper, we introduce new versions of -dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an -duality result between...

Vector quasi-equilibrium problem | [formula omitted]-solution | [formula omitted]-duality | Set-valued map | Vector optimization problem | ε{lunate}-duality | ε{lunate}-solution | EXISTENCE | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | MULTIOBJECTIVE OPTIMIZATION | SET-VALUED MAPS | epsilon-duality | PROPER EFFICIENCY | NOTION | VARIATIONAL-INEQUALITIES | MATHEMATICS | epsilon-solution | Nonlinearity | Approximation | Maps | Vectors (mathematics) | Mathematical analysis | Optimization

Vector quasi-equilibrium problem | [formula omitted]-solution | [formula omitted]-duality | Set-valued map | Vector optimization problem | ε{lunate}-duality | ε{lunate}-solution | EXISTENCE | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | MULTIOBJECTIVE OPTIMIZATION | SET-VALUED MAPS | epsilon-duality | PROPER EFFICIENCY | NOTION | VARIATIONAL-INEQUALITIES | MATHEMATICS | epsilon-solution | Nonlinearity | Approximation | Maps | Vectors (mathematics) | Mathematical analysis | Optimization

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 02/2010, Volume 31, Issue 1, pp. 78 - 95

In this paper, I introduce two kinds of ε-subgradients-ε-Pareto subgradients and ε-Benson proper subgradients-for set-valued maps. I give sufficient conditions...

ε-Efficient solution | ε-Optimality condition | ε-Benson proper efficient solution | 90C46 | 90C29 | ε-Benson proper subdifferentials | ε-Subgradient | 90C26 | Set-valued map | ε-Benson proper subgradient | Vector optimization problem | Benson proper subgradient | MATHEMATICS, APPLIED | epsilon-Benson proper subgradient | epsilon-Optimality condition | epsilon-Efficient solution | CONSTRAINTS | DUALITY | SUBDIFFERENTIALS | epsilon-Benson proper subdifferentials | epsilon-Subgradient | EPIDERIVATIVES | epsilon-Benson proper efficient solution

ε-Efficient solution | ε-Optimality condition | ε-Benson proper efficient solution | 90C46 | 90C29 | ε-Benson proper subdifferentials | ε-Subgradient | 90C26 | Set-valued map | ε-Benson proper subgradient | Vector optimization problem | Benson proper subgradient | MATHEMATICS, APPLIED | epsilon-Benson proper subgradient | epsilon-Optimality condition | epsilon-Efficient solution | CONSTRAINTS | DUALITY | SUBDIFFERENTIALS | epsilon-Benson proper subdifferentials | epsilon-Subgradient | EPIDERIVATIVES | epsilon-Benson proper efficient solution

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 12, pp. e2540 - e2550

In this paper, we consider a convex semidefinite vector optimization problem (SDVP) involving a convex objective vector function, a matrix linear inequality...

A convex semidefinite vector optimization problem | Optimality conditions | Efficient solutions | MATHEMATICS | MATHEMATICS, APPLIED | PROGRAMS | Optimality condition | PROPER EFFICIENCY | Theorems | Mathematical analysis | Inequalities | Nonlinearity | Vectors (mathematics) | Geometric constraints | Optimization

A convex semidefinite vector optimization problem | Optimality conditions | Efficient solutions | MATHEMATICS | MATHEMATICS, APPLIED | PROGRAMS | Optimality condition | PROPER EFFICIENCY | Theorems | Mathematical analysis | Inequalities | Nonlinearity | Vectors (mathematics) | Geometric constraints | Optimization

Journal Article

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