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Generalized Lagrangian Duality in Set-valued Vector Optimization via Abstract Subdifferential
In this paper, we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential. We first introduce a...
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Second-order optimality conditions for set-valued optimization problems under the set criterion
This paper investigates second-order optimality conditions for general constrained set-valued optimization problems in normed vector spaces under the...
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Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions
In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A...
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Pareto epsilon-subdifferential sum rule for set-valued map**s and applications to set optimization
In this paper, we are mainly concerned with a rule for efficient (Pareto) approximate subdifferential, concerning the sum of two cone-convex...
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Directional Derivative and Subgradient of Cone-Convex Set-Valued Map**s with Applications in Set Optimization Problems
In this paper, we introduce a new directional derivative and subgradient of set-valued map**s by using a nonlinear scalarizing function. We obtain...
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Global well-posedness of set-valued optimization with application to uncertain problems
Well-posedness for optimization problems is a well-known notion and has been studied extensively for scalar, vector and set-valued optimization...
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Pointwise well-posedness of a set-valued optimization problem at a weak solution
Well-posedness of optimization problems is a well explored topic in scalar, vector, and set-valued optimization literature. Pointwise well-posedness...
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Approximate Weak Minimal Solutions of Set-Valued Optimization Problems
This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria. The...
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Directional derivatives and subdifferentials for set-valued maps applied to set optimization
We present a general method to devise directional derivatives and subdifferentials for set-valued maps that generalize the corresponding...
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Probability Functions Generated by Set-Valued Map**s: A Study of First Order Information
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order...
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Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence
We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the...
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A Note on Pointwise Well-Posedness of Set-Valued Optimization Problems
Well-posedness for optimization problems is a well-known notion and has been studied extensively for scalar, vector, and set-valued optimization...
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Nonlinear analysis in p-vector spaces for single-valued 1-set contractive map**s
The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued map**s under the framework of p -vector...
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Painlevé-Kuratowski convergence of minimal solutions for set-valued optimization problems via improvement sets
The aim of this paper is to explore the stability of (weak)-minimal solutions for set-valued optimization problems via improvement sets. Firstly, the...
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Sequential Pareto Subdifferential Sum Rule for Convex Set-Valued Map**s and Applications
The aim of this paper is to provide a general description of the Pareto subdifferential (weak and proper) of the sum of two cone-convex set-valued...
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Using ρ-cone arcwise connectedness on parametric set-valued optimization problems
Within the inquiry about work, we explore a parametric set-valued optimization problem, where the objective as well as constraint maps are...
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A Notion of Fenchel Conjugate for Set-Valued Map**s
In this paper, we present a novel concept of the Fenchel conjugate for set-valued map**s and investigate its properties in finite and infinite...
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Higher-order optimality conditions of robust Benson proper efficient solutions in uncertain vector optimization problems
In this article, we study higher-order optimality conditions of robust Benson proper efficient solutions in uncertain vector optimization problems....
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Characteristic curves for Set-Valued Hamilton-Jacobi Equations
The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problem arises from a calculus of variations’ problem with a...