Taiwanese Journal of Mathematics, ISSN 1027-5487, 10/2016, Volume 20, Issue 5, pp. 1149 - 1173

The aim of this paper is to present new results on the convergence of relative Pareto efficient sets and the lower semicontinuity of relative Pareto efficient point multifunctions under perturbations...

Efficient point | Mathematical vectors | Mathematical theorems | Banach space | Pareto efficiency | Topological vector spaces | Lower semicontinuity | Relative containment property | Stability | Kuratowski-Painlevé convergence | Relative Pareto efficient | MATHEMATICS | Kuratowski-Painleve convergence | CONTINUITY | MINIMAL POINTS | MULTIFUNCTIONS | VECTOR OPTIMIZATION PROBLEMS | MULTIOBJECTIVE PROBLEMS | OPTIMALITY

Efficient point | Mathematical vectors | Mathematical theorems | Banach space | Pareto efficiency | Topological vector spaces | Lower semicontinuity | Relative containment property | Stability | Kuratowski-Painlevé convergence | Relative Pareto efficient | MATHEMATICS | Kuratowski-Painleve convergence | CONTINUITY | MINIMAL POINTS | MULTIFUNCTIONS | VECTOR OPTIMIZATION PROBLEMS | MULTIOBJECTIVE PROBLEMS | OPTIMALITY

Journal Article

2.
Full Text
Set convergence of non-convex vector optimization problem with variable ordering structure

Optimization: International Workshop on Nonlinear and Variational Analysis 2018. Guest Editors: Marius Durea, Akhtar A. Khan, Elisabeth Köbis, Nguyen Dong Yen & Jen-Chih Yao, ISSN 0233-1934, 02/2020, Volume 69, Issue 2, pp. 329 - 344

The aim of this paper is to establish the convergence of a non-convex vector optimization problem, which is a quasiconnected vector optimization problem with respect to the perturbation of feasible...

minimal and efficient point | Kuratowski-Painlevé convergence | quasiconnected function | Non-convex vector optimization | cone-sectionwise connected set | 49K40 | 90C29 | 90C26 | Kuratowski–Painlevé convergence | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILITY | Optimization | Perturbation | Convergence

minimal and efficient point | Kuratowski-Painlevé convergence | quasiconnected function | Non-convex vector optimization | cone-sectionwise connected set | 49K40 | 90C29 | 90C26 | Kuratowski–Painlevé convergence | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILITY | Optimization | Perturbation | Convergence

Journal Article

Journal of optimization theory and applications, ISSN 0022-3239, 2012, Volume 155, Issue 3, pp. 941 - 961

.... We establish the Kuratowski–Painlevé set-convergence of the minimal solution sets of a family of perturbed problems to the corresponding minimal solution set of the vector problem, where the perturbations are performed on both the...

Gamma convergence | Kuratowski–Painlevé set-convergence | Calculus of Variations and Optimal Control; Optimization | Efficiency | Operations Research/Decision Theory | Scalarization | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Quasi cone-convexity | Optimization | Kuratowski-Painlevé set-convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Kuratowski-Painleve set-convergence | CONVERGENCE | POINTS | VECTOR | Studies | Set theory | Convergence | Stability | Mathematical analysis | Scalars | Perturbation | Vectors (mathematics) | Preserving

Gamma convergence | Kuratowski–Painlevé set-convergence | Calculus of Variations and Optimal Control; Optimization | Efficiency | Operations Research/Decision Theory | Scalarization | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Quasi cone-convexity | Optimization | Kuratowski-Painlevé set-convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Kuratowski-Painleve set-convergence | CONVERGENCE | POINTS | VECTOR | Studies | Set theory | Convergence | Stability | Mathematical analysis | Scalars | Perturbation | Vectors (mathematics) | Preserving

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2012, Volume 155, Issue 2, pp. 492 - 506

... function and the feasible set. The Kuratowski–Painlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems...

Calculus of Variations and Optimal Control; Optimization | Efficiency | Operations Research/Decision Theory | Weak efficiency | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Kuratowski–Painlevé convergence | Proper efficiency | Optimization | Proper quasi cone-convexity | Kuratowski-Painlevé convergence | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EPSILON-VARIATIONAL PRINCIPLE | SENSITIVITY-ANALYSIS | CONVERGENCE | WELL-POSEDNESS | Universities and colleges | Stability | Vectors (mathematics) | Mathematical analysis | Images

Calculus of Variations and Optimal Control; Optimization | Efficiency | Operations Research/Decision Theory | Weak efficiency | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Kuratowski–Painlevé convergence | Proper efficiency | Optimization | Proper quasi cone-convexity | Kuratowski-Painlevé convergence | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EPSILON-VARIATIONAL PRINCIPLE | SENSITIVITY-ANALYSIS | CONVERGENCE | WELL-POSEDNESS | Universities and colleges | Stability | Vectors (mathematics) | Mathematical analysis | Images

Journal Article

1993, Mathematics and its applications, ISBN 9780792325314, Volume 268, xi, 340

Book

Optimization, ISSN 1029-4945, 2018, Volume 68, Issue 4, pp. 833 - 852

The main aim of this paper is to establish stability in set optimization in terms of convergence of a sequence of solution sets of perturbed set optimization problems to the solution set...

Hausdorff convergence | convergence | stability | strict quasiconvexity | 90C31 | 49J53 | 90C29 | EXISTENCE | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | LAGRANGIAN-DUALITY | SCALARIZATION | CONVERGENCE | Formulations | Continuity | Stability | Automobile parking | Optimization | Convergence

Hausdorff convergence | convergence | stability | strict quasiconvexity | 90C31 | 49J53 | 90C29 | EXISTENCE | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | LAGRANGIAN-DUALITY | SCALARIZATION | CONVERGENCE | Formulations | Continuity | Stability | Automobile parking | Optimization | Convergence

Journal Article

Journal of Convex Analysis, ISSN 0944-6532, 2001, Volume 8, Issue 1, pp. 279 - 289

Given a sequence [T-n] of nonempty closed sets Kuratowski-Painleve convergent to the empty set in a noncompact metrizable space X, we show not only that there...

Metric mode of convergence to infinity | Bornology | Kuratowski-painlevé convergence | Uc space | Bounded set | Metric bornology | MATHEMATICS | Kuratowski-Painleve convergence | bornology | bounded set | metric bornology | metric mode of convergence to infinity | UC space

Metric mode of convergence to infinity | Bornology | Kuratowski-painlevé convergence | Uc space | Bounded set | Metric bornology | MATHEMATICS | Kuratowski-Painleve convergence | bornology | bounded set | metric bornology | metric mode of convergence to infinity | UC space

Journal Article

8.
Full Text
Fell type topologies of quasi-pseudo-metric spaces and the Kuratowski-Painlevé convergence

Applied general topology, ISSN 1576-9402, 04/2001, Volume 2, Issue 1, pp. 9 - 25

... convergence in the bitopological setting.

Fell topology | Wijsman topology | Double topological space | Kuratowski-Painlevé convergence | Quasi-pseudo-metric

Fell topology | Wijsman topology | Double topological space | Kuratowski-Painlevé convergence | Quasi-pseudo-metric

Journal Article

Journal of Convex Analysis, ISSN 0944-6532, 2010, Volume 17, Issue 3-4, pp. 805 - 826

...(X) of a Hausdorff space X that are sequentially equivalent to classical Kuratowski-Painleve convergence K...

Hit-and-miss topology | Hyperspace | Sequential modification | Modification | Subsequential selector | Fell topology | Kuratowski-Painlevé convergence | TIGHTNESS | MATHEMATICS | Kuratowski-Painleve convergence | hit-and-miss topology | hyperspace | CYRTOLOGIES | sequential modification | modification | subsequential selector | COINCIDENCE | CONSONANCE

Hit-and-miss topology | Hyperspace | Sequential modification | Modification | Subsequential selector | Fell topology | Kuratowski-Painlevé convergence | TIGHTNESS | MATHEMATICS | Kuratowski-Painleve convergence | hit-and-miss topology | hyperspace | CYRTOLOGIES | sequential modification | modification | subsequential selector | COINCIDENCE | CONSONANCE

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 09/1994, Volume 37, Issue 3, pp. 294 - 300

... of convergence to force epigraphical convergence with respect to the stronger Hausdorff metric and Vietoris topologies?

MATHEMATICS | EPI-CONVERGENCE | FELL TOPOLOGY | KURATOWSKI-PAINLEVE CONVERGENCE | HAUSDORFF DISTANCE | LOWER SEMICONTINUOUS FUNCTION | VIETORIS TOPOLOGY

MATHEMATICS | EPI-CONVERGENCE | FELL TOPOLOGY | KURATOWSKI-PAINLEVE CONVERGENCE | HAUSDORFF DISTANCE | LOWER SEMICONTINUOUS FUNCTION | VIETORIS TOPOLOGY

Journal Article

Set-Valued Analysis, ISSN 0927-6947, 03/1994, Volume 2, Issue 1-2, pp. 207 - 218

Journal Article

Topology and its Applications, ISSN 0166-8641, 1996, Volume 70, Issue 2, pp. 213 - 243

... KuratowskiPainlevé convergence of an arbitrary net of closed subsets of X to some closed set A implies that the same net, considered as a net of points...

Hyperspace | Upper Kuratowski-Painlevé convergence | Upper Kuratowski topology | Metric space | Fell topology | Kuratowski topology | Kuratowski-Painlevé convergence | Topologization of convergence | Kuratowski-Painlevé | Convergence | Upper kuratowski topology | topologization of convergence | metric space | Kuratowski-Painleve convergence | upper Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | hyperspace | upper Kuratowski topology

Hyperspace | Upper Kuratowski-Painlevé convergence | Upper Kuratowski topology | Metric space | Fell topology | Kuratowski topology | Kuratowski-Painlevé convergence | Topologization of convergence | Kuratowski-Painlevé | Convergence | Upper kuratowski topology | topologization of convergence | metric space | Kuratowski-Painleve convergence | upper Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | hyperspace | upper Kuratowski topology

Journal Article

Pacific Journal of Optimization, ISSN 1348-9151, 09/2008, Volume 4, Issue 3, pp. 621 - 628

Convex subdifferential calculus obeys various rules possibly involving approximate subdifferentials. Some of these rules concern nonconvex functions like for...

Legendre-Fenchel conjugate Kuratowski-Painlevé convergence | Argmin calculus | Subdifferential calculus | Convex analysis | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | subdifferential calculus | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | convex analysis | argmin calculus | Legendre-Fenchel conjugate

Legendre-Fenchel conjugate Kuratowski-Painlevé convergence | Argmin calculus | Subdifferential calculus | Convex analysis | Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | subdifferential calculus | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | convex analysis | argmin calculus | Legendre-Fenchel conjugate

Journal Article

Optimization, ISSN 0233-1934, 01/2002, Volume 51, Issue 1, pp. 31 - 45

In this paper, we define the Mosco convergence and Kuratowski-Painleve (P.K.) convergence for set-valued mapping sequence F n...

Kuratowski-Painleve convergence | Stability | Mosco convergence | Set-valued mapping | Ekeland's variational principle for set-valued mappings

Kuratowski-Painleve convergence | Stability | Mosco convergence | Set-valued mapping | Ekeland's variational principle for set-valued mappings

Journal Article

Topology and its Applications, ISSN 0166-8641, 2000, Volume 104, Issue 1, pp. 27 - 38

A topological space is called consonant if, on the set of all closed subsets of X, the co-compact topology coincides with the upper Kuratowski topology. For a...

P-set | Hereditarily Baire space | Co-compact topology | Filter | Consonance | Upper Kuratowski–Painlevé convergence | Hereditarily baire space | Upper kuratowski-painlevé | Convergence | filter | MATHEMATICS | upper Kuratowski-Painleve convergence | FUNCTION-SPACES | TOPOLOGIES | MATHEMATICS, APPLIED | co-compact topology | hereditarily Baire space | SETS | consonance | CP(X) | Mathematics | General Topology

P-set | Hereditarily Baire space | Co-compact topology | Filter | Consonance | Upper Kuratowski–Painlevé convergence | Hereditarily baire space | Upper kuratowski-painlevé | Convergence | filter | MATHEMATICS | upper Kuratowski-Painleve convergence | FUNCTION-SPACES | TOPOLOGIES | MATHEMATICS, APPLIED | co-compact topology | hereditarily Baire space | SETS | consonance | CP(X) | Mathematics | General Topology

Journal Article

Houston Journal of Mathematics, ISSN 0362-1588, 2003, Volume 29, Issue 2, pp. 325 - 335

By Cld(F) (X), we denote the hyperspace of non-empty closed sets of a locally compact metrizable space X with the Fell topology. Let Cont(F) (X) be its...

The Fell topology | The Hilbert cube | Z-sets | Connected closed sets | Continua | Ends | Kuratowski-Painlevé convergence | Freudenthal compactification | MATHEMATICS | Kuratowski-Painleve convergence | continua | the Hilbert cube | connected closed sets | ends

The Fell topology | The Hilbert cube | Z-sets | Connected closed sets | Continua | Ends | Kuratowski-Painlevé convergence | Freudenthal compactification | MATHEMATICS | Kuratowski-Painleve convergence | continua | the Hilbert cube | connected closed sets | ends

Journal Article

OPTIMIZATION, ISSN 0233-1934, 02/2002, Volume 51, Issue 1, pp. 31 - 45

In this paper, we define the Mosco convergence and Kuratowski-Painleve (P.K.) convergence for set-valued mapping sequence F-n...

Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Ekeland's variational principle for set-valued mappings | set-valued mapping | Mosco convergence | stability

Kuratowski-Painleve convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Ekeland's variational principle for set-valued mappings | set-valued mapping | Mosco convergence | stability

Journal Article

杭州师范大学学报：自然科学版, ISSN 1674-232X, 2014, Volume 13, Issue 2, pp. 186 - 191

Journal Article

Optimization, ISSN 0233-1934, 01/1990, Volume 21, Issue 4, pp. 521 - 534

.... Topological and metric results are given. Applications to variational convergence, in particular to epi-convergence of convex functions, are presented.

epieonvergence | Secondary:52 A 50 | Primary:49 A 50 | Kuratowski-Painlevé limits | Hausdorff metric | convex set-valued maps | Convex set-valued maps | Epiconvergence

epieonvergence | Secondary:52 A 50 | Primary:49 A 50 | Kuratowski-Painlevé limits | Hausdorff metric | convex set-valued maps | Convex set-valued maps | Epiconvergence

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2017, Volume 174, Issue 1, pp. 32 - 46

In the paper, a Lagrange optimal control problem governed by a fractional Dirichlet problem with the Riemann–Liouville derivative is considered. To begin with,...

Kuratowski–Painlevé limit | Fractional optimal control problem | 35A15 | Fractional Lagrange problem | 26A33 | Mathematics | Theory of Computation | Continuous dependence | Optimization | Calculus of Variations and Optimal Control; Optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 49J15 | Fractional Dirichlet problem | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Kuratowski-Painleve limit | EVOLUTION-EQUATIONS | FORMULATION | SOBOLEV TYPE | CONTROLLABILITY | Computer science | Dirichlet problem | Optimal control | Continuity (mathematics)

Kuratowski–Painlevé limit | Fractional optimal control problem | 35A15 | Fractional Lagrange problem | 26A33 | Mathematics | Theory of Computation | Continuous dependence | Optimization | Calculus of Variations and Optimal Control; Optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 49J15 | Fractional Dirichlet problem | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Kuratowski-Painleve limit | EVOLUTION-EQUATIONS | FORMULATION | SOBOLEV TYPE | CONTROLLABILITY | Computer science | Dirichlet problem | Optimal control | Continuity (mathematics)

Journal Article

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