scholarly journals Optimality criteria in set-valued optimization

2003 ◽  
Vol 75 (2) ◽  
pp. 221-232 ◽  
Author(s):  
C. S. Lalitha ◽  
J. Dutta ◽  
Misha G. Govil
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Convex Set ◽  
Necessary Optimality Conditions ◽  
Optimality Criteria ◽  
New Class ◽  
Invex Set

AbstractThe main aim of this paper is to obtain optimality conditions for a constrained set-valued optimization problem. The concept of Clarke epiderivative is introduced and is used to derive necessary optimality conditions. In order to establish sufficient optimality criteria we introduce a new class of set-valued maps which extends the class of convex set-valued maps and is different from the class of invex set-valued maps.

scholarly journals Necessary Optimality Conditions in Isoperimetric Constrained Optimal Control Problems

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1380
Author(s):  
Silviu-Aurelian Urziceanu
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Level Sets ◽  
Optimization Problem ◽  
Optimal Control Problems ◽  
Adjoint Equation ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
New Class

In this paper, we focus on a new class of optimal control problems governed by a simple integral cost functional and isoperimetric-type constraints (constant level sets of some simple integral functionals). By using the notions of a variational differential system and adjoint equation, necessary optimality conditions are established for a feasible solution in the considered optimization problem. More precisely, under simplified hypotheses and using a modified Legendrian duality, we establish a maximum principle for the considered optimization problem.

scholarly journals A Class of SemilocalE-Preinvex Functions and Its Applications in Nonlinear Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hehua Jiao ◽  
Sanyang Liu ◽  
Xinying Pai
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions ◽  
Convex Set ◽  
Basic Properties ◽  
New Class ◽  
Duality Results ◽  
Invex Set ◽  
Preinvex Functions ◽  
Class Of Functions

A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

scholarly journals Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

2020 ◽  
Author(s):  
Mohsine Jennane ◽  
El Mostafa Kalmoun ◽  
Lahoussine Lafhim
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Convexity Assumption ◽  
Locally Lipschitz ◽  
Infinite Programming ◽  
Asymptotic Convexity ◽  
Interval Valued

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide  Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions  under the asymptotic convexity assumption.

scholarly journals Optimality and duality in set-valued optimization utilizing limit sets

2018 ◽  
Vol 16 (1) ◽  
pp. 1128-1139
Author(s):  
Xiangyu Kong ◽  
Yinfeng Zhang ◽  
GuoLin Yu
Keyword(s):  
Optimality Conditions ◽  
Duality Theory ◽  
Optimization Problem ◽  
Convex Set ◽  
Sufficient Optimality Conditions ◽  
Constraint Optimization ◽  
Limit Sets ◽  
Optimality And Duality ◽  
Wolfe Type Dual ◽  
Necessary And Sufficient

AbstractThis paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

scholarly journals Using necessary optimality conditions for acceleration of the nonuniform covering optimization method

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Yury Evtushenko ◽  
Mikhail Posypkin
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Necessary Optimality Conditions ◽  
Optimization Method ◽  
Upper And Lower Bounds ◽  
Test Problems ◽  
Covering Method ◽  
Computer Resources ◽  
Uniform Covering

Abstract Paper deals with the non-uniform covering method that is aimed at deterministic global optimization. This method finds a feasible solution to the optimization problem numerically and proves that the obtained solution differs from the optimal by no more than a given accuracy. Numerical proof consists of constructing a set of covering sets - the coverage. The number of elements in the coverage can be very large and even exceed the total amount of available computer resources. Basic method of coverage construction is the comparison of upper and lower bounds on the value of the objective function. In this work we propose to use necessary optimality conditions of first and second order for reducing the search for boxconstrained problems. We provide the algorithm description and prove its correctness. The efficiency of the proposed approach is studied on test problems.

scholarly journals A class of semilocal E-preinvex maps in Banach spaces with applications to nondifferentiable vector optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 1-10
Author(s):  
Hehua Jiao
Keyword(s):  
Optimality Conditions ◽  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Basic Properties ◽  
New Class ◽  
Duality Results

In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces is introduced for a nondifferentiable vector optimization problem with restrictions of inequalities and some of its basic properties are studied. Furthermore, as its applications, some optimality conditions and duality results are established for a nondifferentiable vector optimization under the aforesaid maps assumptions.

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