Journal of Global Optimization, ISSN 0925-5001, 11/2013, Volume 57, Issue 3, pp. 951 - 968

We consider Ekeland’s variational principle for multivalued maps. Instead of dealing with directional perturbations in a direction of the positive cone...

Relaxed semicontinuity | Minimal elements | 90C48 | 58E17 | Optimization | Economics / Management Science | Kuroiwa’s minimizers | Pareto minimizers | 49J53 | Operations Research/Decision Theory | Set perturbations | 65K10 | 58E30 | Computer Science, general | Ekeland’s variational principle | Real Functions | Ekeland's variational principle | Kuroiwa's minimizers | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FIXED-POINT THEORY | VECTOR EQUILIBRIUM PROBLEMS | VALUED MAPPINGS | OPTIMIZATION | Studies | Maps | Mathematical analysis | Images | Perturbation | Variational principles | Dealing

Relaxed semicontinuity | Minimal elements | 90C48 | 58E17 | Optimization | Economics / Management Science | Kuroiwa’s minimizers | Pareto minimizers | 49J53 | Operations Research/Decision Theory | Set perturbations | 65K10 | 58E30 | Computer Science, general | Ekeland’s variational principle | Real Functions | Ekeland's variational principle | Kuroiwa's minimizers | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FIXED-POINT THEORY | VECTOR EQUILIBRIUM PROBLEMS | VALUED MAPPINGS | OPTIMIZATION | Studies | Maps | Mathematical analysis | Images | Perturbation | Variational principles | Dealing

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 7

In this paper, a new version of Ekeland’s variational principle by using the concept of τ...

Analysis | equilibrium problem | Mathematics, general | Mathematics | bounded below | Applications of Mathematics | Ekeland’s variational principle | τ -distance | lower semicontinuous function | τ-distance | Research

Analysis | equilibrium problem | Mathematics, general | Mathematics | bounded below | Applications of Mathematics | Ekeland’s variational principle | τ -distance | lower semicontinuous function | τ-distance | Research

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2012, Volume 389, Issue 1, pp. 1 - 14

Motivated by the recent work on conditional risk measures, this paper studies the Ekelandʼs variational principle for a proper, lower semicontinuous and lower bounded L...

Random metric space | Random normed module | [formula omitted]-valued function | Bishop–Phelps theorem | Ekelandʼs variational principle | Lower semicontinuity | Bishop-Phelps theorem | 0-valued function | Ekeland's variational principle

Random metric space | Random normed module | [formula omitted]-valued function | Bishop–Phelps theorem | Ekelandʼs variational principle | Lower semicontinuity | Bishop-Phelps theorem | 0-valued function | Ekeland's variational principle

Journal Article

数学学报：英文版, ISSN 1439-8516, 2013, Volume 29, Issue 9, pp. 1655 - 1678

In this paper, by using p-distances on uniform spaces, we establish a general vectorial Ekeland variational principle （in short EVP...

矢量 | 一致空间 | 局部凸拓扑向量空间 | Ekeland变分原理 | 目标函数 | 距离和 | EVP | Caristi不动点定理 | 46A03 | 49J40 | Vectorial Ekeland’s variational principle | vectorial Takahashi’s minimization theorem | p-distance | Mathematics, general | Mathematics | 58E30 | 46N10 | vectorial Caristi’s fixed point theorem | Gerstewitz’s function | vectorial Takahashi's minimization theorem | Vectorial Ekeland's variational principle | vectorial Caristi's fixed point theorem | Gerstewitz's function | LOCALLY CONVEX-SPACES | MATHEMATICS, APPLIED | COMPLETENESS | NUCLEAR CONES | PRODUCT-SPACES | MATHEMATICS | DANES DROP THEOREM | FIXED-POINT THEOREMS | UNIFORM-SPACES | OPTIMIZATION | EFFICIENCY | EQUIVALENT FORMULATIONS | Studies | Theorems | Mathematical models | Functions (mathematics) | Equivalence | Perturbation methods | Mathematical analysis | Completeness | Complement | Variational principles

矢量 | 一致空间 | 局部凸拓扑向量空间 | Ekeland变分原理 | 目标函数 | 距离和 | EVP | Caristi不动点定理 | 46A03 | 49J40 | Vectorial Ekeland’s variational principle | vectorial Takahashi’s minimization theorem | p-distance | Mathematics, general | Mathematics | 58E30 | 46N10 | vectorial Caristi’s fixed point theorem | Gerstewitz’s function | vectorial Takahashi's minimization theorem | Vectorial Ekeland's variational principle | vectorial Caristi's fixed point theorem | Gerstewitz's function | LOCALLY CONVEX-SPACES | MATHEMATICS, APPLIED | COMPLETENESS | NUCLEAR CONES | PRODUCT-SPACES | MATHEMATICS | DANES DROP THEOREM | FIXED-POINT THEOREMS | UNIFORM-SPACES | OPTIMIZATION | EFFICIENCY | EQUIVALENT FORMULATIONS | Studies | Theorems | Mathematical models | Functions (mathematics) | Equivalence | Perturbation methods | Mathematical analysis | Completeness | Complement | Variational principles

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 3/2011, Volume 49, Issue 3, pp. 381 - 396

... of Ekeland’s variational principle and equivalent formulations.

Lower closedness | Locally convex spaces | K -lower semicontinity from above | Operations Research/Decision Theory | Computer Science, general | Ekeland’s variational principle | Weak τ -functions | Optimization | Economics / Management Science | Real Functions | K-lower semicontinity from above | Weak τ-functions | Ekeland's variational principle | EXISTENCE | MATHEMATICS, APPLIED | VARIANTS | Weak tau-functions | FIXED-POINT THEOREMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAPS | DROP THEOREM | OPTIMIZATION | COMPLETE METRIC-SPACES | CONE | Studies

Lower closedness | Locally convex spaces | K -lower semicontinity from above | Operations Research/Decision Theory | Computer Science, general | Ekeland’s variational principle | Weak τ -functions | Optimization | Economics / Management Science | Real Functions | K-lower semicontinity from above | Weak τ-functions | Ekeland's variational principle | EXISTENCE | MATHEMATICS, APPLIED | VARIANTS | Weak tau-functions | FIXED-POINT THEOREMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAPS | DROP THEOREM | OPTIMIZATION | COMPLETE METRIC-SPACES | CONE | Studies

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 3/2019, Volume 35, Issue 3, pp. 297 - 320

....: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904–937 (2014)]. By using the generalized...

partial order principle | convex cone | 46A03 | 49J53 | Ekeland variational principle | Mathematics, general | 65K10 | Mathematics | 58E30 | ε -efficient solutions in the sense of Németh | Gerstewitz’s function | ε-efficient solutions in the sense of Németh | Economic models | Mathematical analysis

partial order principle | convex cone | 46A03 | 49J53 | Ekeland variational principle | Mathematics, general | 65K10 | Mathematics | 58E30 | ε -efficient solutions in the sense of Németh | Gerstewitz’s function | ε-efficient solutions in the sense of Németh | Economic models | Mathematical analysis

Journal Article

数学学报：英文版, ISSN 1439-8516, 2017, Volume 33, Issue 6, pp. 775 - 792

In my former paper ＂A pre-order principle and set-valued Ekeland variational principle...

弱T-函数 | 凸子集 | 广义距离 | 扰动 | 阿波罗 | 集值映射 | 总裁 | Ekeland变分原理 | Ekeland variational principle | set-valued map | vector optimization | Pre-order principle | perturbation | locally convex space | EXISTENCE | MATHEMATICS, APPLIED | MATHEMATICS | THEOREMS | UNIFORM-SPACES | MAPPINGS | COMPLETE METRIC-SPACES | Formulations | Set theory | Perturbation methods | Variational principles | Mathematical analysis

弱T-函数 | 凸子集 | 广义距离 | 扰动 | 阿波罗 | 集值映射 | 总裁 | Ekeland变分原理 | Ekeland variational principle | set-valued map | vector optimization | Pre-order principle | perturbation | locally convex space | EXISTENCE | MATHEMATICS, APPLIED | MATHEMATICS | THEOREMS | UNIFORM-SPACES | MAPPINGS | COMPLETE METRIC-SPACES | Formulations | Set theory | Perturbation methods | Variational principles | Mathematical analysis

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 5/2012, Volume 153, Issue 2, pp. 280 - 297

... Ekeland’s variational principle for Pareto minimizers of set-valued mappings and underlying minimal-element principles...

Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Minimal elements | K -lower semicontinuity | Mathematics | Theory of Computation | ( k 0 , K )-lower semicontinuity from above | Applications of Mathematics | Engineering, general | Ekeland’s variational principle | Weak τ -functions | Optimization | K)-lower semicontinuity from above | K-lower semicontinuity | Weak τ-functions | Ekeland's variational principle | EXISTENCE | MATHEMATICS, APPLIED | Weak tau-functions | FIXED-POINT THEORY | VECTOR EQUILIBRIUM PROBLEMS | (k, K)-lower semicontinuity from above | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERALIZED DISTANCE | THEOREMS | OPTIMIZATION | COMPLETE METRIC-SPACES | EQUIVALENT FORMULATIONS | Studies | Mapping

Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Minimal elements | K -lower semicontinuity | Mathematics | Theory of Computation | ( k 0 , K )-lower semicontinuity from above | Applications of Mathematics | Engineering, general | Ekeland’s variational principle | Weak τ -functions | Optimization | K)-lower semicontinuity from above | K-lower semicontinuity | Weak τ-functions | Ekeland's variational principle | EXISTENCE | MATHEMATICS, APPLIED | Weak tau-functions | FIXED-POINT THEORY | VECTOR EQUILIBRIUM PROBLEMS | (k, K)-lower semicontinuity from above | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERALIZED DISTANCE | THEOREMS | OPTIMIZATION | COMPLETE METRIC-SPACES | EQUIVALENT FORMULATIONS | Studies | Mapping

Journal Article

Topology and its Applications, ISSN 0166-8641, 2011, Volume 158, Issue 8, pp. 1073 - 1084

In this paper we prove a quasi-metric version of Ekeland Variational Principle and study its connections with the completeness properties of the underlying quasi-metric space...

Caristi–Kirkʼs fixed point theorem | Ekeland Variational Principle | Left (right) K-completeness | Clarkeʼs fixed point theorem | Quasi-metric space | Caristi-Kirk's fixed point theorem | 47H10 | 54E50 | 54E55 | 54E15 | 58E30 | Clarke's fixed point theorem | 49N99 | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | SETS

Caristi–Kirkʼs fixed point theorem | Ekeland Variational Principle | Left (right) K-completeness | Clarkeʼs fixed point theorem | Quasi-metric space | Caristi-Kirk's fixed point theorem | 47H10 | 54E50 | 54E55 | 54E15 | 58E30 | Clarke's fixed point theorem | 49N99 | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | SETS

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 4/2012, Volume 28, Issue 4, pp. 717 - 726

By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005...

Mathematics, general | 65K10 | Mathematics | set-valued map | Caristi-Kirk’s fixed point theorem | 58E30 | Ekeland’s variational principle | 46N10 | locally convex space | Takahashi’s nonconvex minimization theorem | Caristi-Kirk's fixed point theorem | Takahashi's nonconvex minimization theorem | Ekeland's variational principle | EXISTENCE | MATHEMATICS, APPLIED | VARIANTS | SPACES | MATHEMATICS | FIXED-POINT THEOREMS | DROP THEOREM | MAPPINGS | OPTIMIZATION | Studies | Mapping | Mathematical analysis | Calculus of variations | Theorems | Approximation | Equivalence | Proving | Minimization | Variational principles | Optimization

Mathematics, general | 65K10 | Mathematics | set-valued map | Caristi-Kirk’s fixed point theorem | 58E30 | Ekeland’s variational principle | 46N10 | locally convex space | Takahashi’s nonconvex minimization theorem | Caristi-Kirk's fixed point theorem | Takahashi's nonconvex minimization theorem | Ekeland's variational principle | EXISTENCE | MATHEMATICS, APPLIED | VARIANTS | SPACES | MATHEMATICS | FIXED-POINT THEOREMS | DROP THEOREM | MAPPINGS | OPTIMIZATION | Studies | Mapping | Mathematical analysis | Calculus of variations | Theorems | Approximation | Equivalence | Proving | Minimization | Variational principles | Optimization

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2012, Volume 2012, Issue 1, pp. 1 - 11

In this paper, we deal with a vectorial form of Ekeland-type variational principle for multivalued bioperator whose domain is a complete metric space and its range is a subset of a locally convex...

vector variational principle | Mathematical and Computational Biology | Analysis | countably orderable sets | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | Ekeland’s variational principle | Ekeland's variational principle | Vector variational principle | Countably orderable sets | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEORY | THEOREMS | OPTIMIZATION | EQUILIBRIUM PROBLEMS | SET-VALUED MAPPINGS | Fixed point theory | Usage | Metric spaces | Variational principles | Theorems | Maps | Arches | Metric space | Mathematical analysis

vector variational principle | Mathematical and Computational Biology | Analysis | countably orderable sets | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | Ekeland’s variational principle | Ekeland's variational principle | Vector variational principle | Countably orderable sets | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEORY | THEOREMS | OPTIMIZATION | EQUILIBRIUM PROBLEMS | SET-VALUED MAPPINGS | Fixed point theory | Usage | Metric spaces | Variational principles | Theorems | Maps | Arches | Metric space | Mathematical analysis

Journal Article

数学学报：英文版, ISSN 1439-8516, 2015, Volume 31, Issue 4, pp. 595 - 614

We give a general vectorial Ekeland＇s variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space...

矢量 | 实线性空间 | 变量设置 | Ekeland变分原理 | Caristi | 目标函数 | F型拓扑空间 | 不动点定理 | Vectorial Ekeland’s variational principle | direction of perturbation | pre-ordered linear space | F-type topological space | locally convex space | LOCALLY CONVEX-SPACES | MATHEMATICS, APPLIED | DISTANCE | DENSITY | MATHEMATICS | Vectorial Ekeland's variational principle | THEOREMS | OPTIMIZATION | EFFICIENCY | EXTREMAL POINTS | Studies | Topological manifolds | Mathematical analysis | Functions (mathematics) | Theorems | Equivalence | Perturbation methods | Topology | Vectors (mathematics) | Variational principles | Optimization

矢量 | 实线性空间 | 变量设置 | Ekeland变分原理 | Caristi | 目标函数 | F型拓扑空间 | 不动点定理 | Vectorial Ekeland’s variational principle | direction of perturbation | pre-ordered linear space | F-type topological space | locally convex space | LOCALLY CONVEX-SPACES | MATHEMATICS, APPLIED | DISTANCE | DENSITY | MATHEMATICS | Vectorial Ekeland's variational principle | THEOREMS | OPTIMIZATION | EFFICIENCY | EXTREMAL POINTS | Studies | Topological manifolds | Mathematical analysis | Functions (mathematics) | Theorems | Equivalence | Perturbation methods | Topology | Vectors (mathematics) | Variational principles | Optimization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 2/2013, Volume 156, Issue 2, pp. 213 - 231

In this paper, we prove a generalized Ekeland-type variational principle for bifunctions, by showing the existence of solution for some generalized optimization problems...

System of equilibrium problems | Zhong type variational principles | Equilibrium problem | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Ekeland-type variational principles | Applications of Mathematics | Engineering, general | Approximate solution | Optimization | SYSTEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Studies | Mathematical problems | Equilibrium | Algorithms | Variational principles | Mathematical analysis | Triangles | Standards

System of equilibrium problems | Zhong type variational principles | Equilibrium problem | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Ekeland-type variational principles | Applications of Mathematics | Engineering, general | Approximate solution | Optimization | SYSTEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Studies | Mathematical problems | Equilibrium | Algorithms | Variational principles | Mathematical analysis | Triangles | Standards

Journal Article

数学学报：英文版, ISSN 1439-8516, 2017, Volume 33, Issue 2, pp. 210 - 234

By using Gerstewitz functions, we establish a new equilibrium version of Ekeland varia- tional principle, which improves the related results by weakening both the lower boundedness and the lower semi...

46A03 | set-valued vector equilibrium problem | Ekeland variational principle | Mathematics, general | lower semi-continuity | Mathematics | lower boundedness | 58E30 | quasi-ordered locally convex space | 91B50 | EXISTENCE | MATHEMATICS, APPLIED | SPACES | FIXED-POINT THEORY | EQUIVALENTS | MATHEMATICS | THEOREMS | MAPPINGS | OPTIMIZATION | Studies | Banach spaces | Functions (mathematics) | Metric space | Existence theorems | Mathematical analysis | Topology | Vectors (mathematics) | Variational principles

46A03 | set-valued vector equilibrium problem | Ekeland variational principle | Mathematics, general | lower semi-continuity | Mathematics | lower boundedness | 58E30 | quasi-ordered locally convex space | 91B50 | EXISTENCE | MATHEMATICS, APPLIED | SPACES | FIXED-POINT THEORY | EQUIVALENTS | MATHEMATICS | THEOREMS | MAPPINGS | OPTIMIZATION | Studies | Banach spaces | Functions (mathematics) | Metric space | Existence theorems | Mathematical analysis | Topology | Vectors (mathematics) | Variational principles

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 7, pp. 1259 - 1280

... of the bifunctions.Then,we give a general version of vectorial Ekeland variational principle（briefly,denoted by EVP...

EXISTENCE | MATHEMATICS, APPLIED | equilibrium problem | Ekeland variational principle | EQUIVALENTS | MATHEMATICS | THEOREMS | system of equilibrium problems | SETS | OPTIMIZATION | sequentially lower complete space | VALUED FUNCTIONS | quasi-ordered locally convex space | COMPLETE METRIC-SPACES | angelic space

EXISTENCE | MATHEMATICS, APPLIED | equilibrium problem | Ekeland variational principle | EQUIVALENTS | MATHEMATICS | THEOREMS | system of equilibrium problems | SETS | OPTIMIZATION | sequentially lower complete space | VALUED FUNCTIONS | quasi-ordered locally convex space | COMPLETE METRIC-SPACES | angelic space

Journal Article

Optimization, ISSN 0233-1934, 10/2016, Volume 65, Issue 10, pp. 1781 - 1789

What happens to the conclusion of the Ekeland variational principle (briefly, EVP) if a considered function is lower semicontinuous not on the whole metric space X but only on...

Gâteaux differentiability | Ekeland variational principle | lower semicontinuity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Gateaux differentiability | Optimization

Gâteaux differentiability | Ekeland variational principle | lower semicontinuity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Gateaux differentiability | Optimization

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 72, Issue 2, pp. 651 - 661

In this paper, we study the Ekeland type variational principle, a Caristi–Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces...

Quasi-optimization problems | Lower semicontinuity | Uniformly spaces | Quasi-equilibrium problems | Caristi–Kirk type fixed point theorem | Quasi-variational inclusion problems | Sequentially lower monotone maps | Ekeland type variational principle | Caristi-Kirk type fixed point theorem | MATHEMATICS, APPLIED | VARIANTS | EXISTENCE THEOREMS | MATHEMATICS | FIXED-POINT | SYSTEMS | EQUILIBRIUM PROBLEMS | Nonlinearity | Theorems | Inclusions | Variational principles | Mathematical analysis

Quasi-optimization problems | Lower semicontinuity | Uniformly spaces | Quasi-equilibrium problems | Caristi–Kirk type fixed point theorem | Quasi-variational inclusion problems | Sequentially lower monotone maps | Ekeland type variational principle | Caristi-Kirk type fixed point theorem | MATHEMATICS, APPLIED | VARIANTS | EXISTENCE THEOREMS | MATHEMATICS | FIXED-POINT | SYSTEMS | EQUILIBRIUM PROBLEMS | Nonlinearity | Theorems | Inclusions | Variational principles | Mathematical analysis

Journal Article

数学学报：英文版, ISSN 1439-8516, 2015, Issue 8, pp. 1289 - 1302

...）]）, we give a new version of vectorial Ekeland＇s variational principle. In the new version, the objective function is defined on a sequentially lower complete space...

局部凸空间 | 向量值 | 拓扑空间 | 重合点定理 | Caristi型 | Ekeland变分原理 | 目标函数 | Caristi不动点定理

局部凸空间 | 向量值 | 拓扑空间 | 重合点定理 | Caristi型 | Ekeland变分原理 | 目标函数 | Caristi不动点定理

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 05/2012, Volume 20, Issue 1, pp. 101 - 112

In this paper we prove a generalized version of the Ekeland variational principle, which is a common generalization of Zhong variational principle and Borwein Preiss Variational principle...

metric spaces | Ekeland variational principle,Zhong variational principle | Borwein Preiss variational principle | Caristi type fixed point | Ekeland variational principle | Metric spaces | Zhong variational principle | Caristi type fixedpoint | MATHEMATICS | MATHEMATICS, APPLIED

metric spaces | Ekeland variational principle,Zhong variational principle | Borwein Preiss variational principle | Caristi type fixed point | Ekeland variational principle | Metric spaces | Zhong variational principle | Caristi type fixedpoint | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article