scholarly journals On optimality conditions for robust weak sharp solution in uncertain optimizations

2020 ◽  
Vol 36 (3) ◽  
pp. 443-452
Author(s):  
JUTAMAS KERDKAEW ◽  
RABIAN WANGKEEREE ◽  
GUE MYUNG LEE
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Generalized Convexity ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Robust Version ◽  
Robust Optimization Problem ◽  
Weak Sharp Solution ◽  
Weak Sharp

In this paper, we investigate the robust optimization problem involving nonsmooth and nonconvex real-valued functions. We firstly establish a necessary condition for the local robust weak sharp solution of considered problem under a constraint qualification. These optimality conditions are presented in terms of multipliers and Mordukhovich subdifferentials of the related functions. Then, by employing the robust version of the (KKT) condition, and some appropriate generalized convexity conditions, we also obtain some sufficient conditions for the global robust weak sharp solutions of the problem. In addition, some examples are presented for illustrating or supporting the results.

On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems

2019 ◽  
Vol 35 (3) ◽  
pp. 417-426 ◽  
Author(s):  
CHANOKSUDA KHANTREE ◽  
RABIAN WANGKEEREE ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Data Uncertainty ◽  
Necessary Condition ◽  
Duality Theorems ◽  
Approximate Form ◽  
Locally Lipschitz ◽  
Approximate Duality

This paper devotes to the quasi ε-solution for robust semi-infinite optimization problems (RSIP) involving a locally Lipschitz objective function and infinitely many locally Lipschitz constraint functions with data uncertainty. Under the fulfillment of robust type Guignard constraint qualification and robust type Kuhn-Tucker constraint qualification, a necessary condition for a quasi ε-solution to problem (RSIP). After introducing the generalized convexity, we give a sufficient optimality for such a quasi ε-solution to problem (RSIP). Finally, we also establish approximate duality theorems in term of Wolfe type which is formulated in approximate form.

scholarly journals Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 12 ◽  
Author(s):  
Xiangkai Sun ◽  
Hongyong Fu ◽  
Jing Zeng
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Sufficient Optimality Conditions ◽  
Convex Constraint ◽  
Approximate Optimality Conditions ◽  
Necessary And Sufficient

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

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 conditions via scalarization for approximate quasi efficiency in multiobjective optimization

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 671-680 ◽  
Author(s):  
Mehrdad Ghaznavi
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Original Problem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Multiobjective Optimization Problem ◽  
Alternative Theorem ◽  
Convexity Assumptions ◽  
Interesting Area

Approximate problems that scalarize and approximate a given multiobjective optimization problem (MOP) became an important and interesting area of research, given that, in general, are simpler and have weaker existence requirements than the original problem. Recently, necessary conditions for approximation of several types of efficiency for MOPs have been obtained through the use of an alternative theorem. In this paper, we use these results in order to extend them to sufficient conditions for approximate quasi (weak, proper) efficiency. For this, we use two scalarization techniques of Tchebycheff type. All the provided results are established without convexity assumptions.

scholarly journals Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wenyan Han ◽  
Guolin Yu ◽  
Tiantian Gong
Keyword(s):  
Optimality Conditions ◽  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Type I ◽  
Generalized Convex Functions ◽  
Alternative Theorem ◽  
Multiobjective Programming Problem

This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established.

scholarly journals Optimality and duality without a constraint qualification for minimax programming

2003 ◽  
Vol 67 (1) ◽  
pp. 121-130 ◽  
Author(s):  
Houchun Zhou ◽  
Wenyu Sun
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dual Model ◽  
Duality Theorems ◽  
Minimax Programming ◽  
Optimality And Duality ◽  
Necessary And Sufficient

Without the need of a constraint qualification, we establish the optimality necessary and sufficient conditions for generalised minimax programming. Using these optimality conditions, we construct a parametric dual model and a parameter-free mixed dual model. Several duality theorems are established.

scholarly journals Generalized convexity in nondifferentiable programming

1984 ◽  
Vol 30 (2) ◽  
pp. 193-218 ◽  
Author(s):  
Bevil M. Glover
Keyword(s):  
Mathematical Programming ◽  
Optimality Conditions ◽  
Programming Problem ◽  
Constraint Qualification ◽  
Generalized Convexity ◽  
Nondifferentiable Programming ◽  
Mathematical Programming Problem ◽  
Sufficient Optimality Conditions ◽  
Cone Constraints ◽  
Necessary And Sufficient

For an abstract mathematical programming problem involving quasidifferentiable cone-constraints we obtain necessary (and sufficient) optimality conditions of the Kuhn-Tucker type without recourse to a constraint qualification. This extends the known results to the non-differentiable setting. To obtain these results we derive several simple conditions connecting various concepts in generalized convexity not requiring differentiability of the functions involved.

scholarly journals Necessary optimality conditions for a fractional multiobjective optimization problem

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
khadija hamdaoui ◽  
mohammed El idrissi ◽  
Fatima zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions

In this paper, we are concerned with a fractional multiobjective optimization problem (P). Using support functions together with a generalized Guignard constraint qualification, we give necessary optimality conditions in terms of convexificators and the Karush-Kuhn-Tucker multipliers. Several intermediate optimization problems have been introduced to help us in our investigation.

scholarly journals Optimality conditions for robust weak sharp efficient solutions of nonsmooth uncertain multiobjective optimization problems

2021 ◽  
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Rattanaporn Wangkeereee
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Nonconvex Functions ◽  
Multiobjective Optimization Problems ◽  
Necessary And Sufficient ◽  
Weak Sharp

AbstractIn this paper, we investigate an uncertain multiobjective optimization problem involving nonsmooth and nonconvex functions. The notion of a (local/global) robust weak sharp efficient solution is introduced. Then, we establish necessary and sufficient optimality conditions for local and/or the robust weak sharp efficient solutions of the considered problem. These optimality conditions are presented in terms of multipliers and Mordukhovich/limiting subdifferentials of the related functions.

Generalized Convexity and Characterization of (Weak) Pareto-Optimality in Nonsmooth Multiobjective Optimization Problems

2015 ◽  
Vol 14 (04) ◽  
pp. 877-899 ◽  
Author(s):  
Majid Soleimani-Damaneh
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Nonsmooth Analysis ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Differential Analysis ◽  
Multiobjective Optimization Problems ◽  
Nonsmooth Multiobjective Optimization

Efforts to characterize optimality in nonsmooth and/or nonconvex optimization problems have made rapid progress in the past four decades. Nonsmooth analysis, which refers to differential analysis in the absence of differentiability, has grown rapidly in recent years, and plays a vital role in functional analysis, information technology, optimization, mechanics, differential equations, decision making, etc. Furthermore, convexity has been increasingly important nowadays in the study of many pure and applied mathematical problems. In this paper, some new connections between three major fields, nonsmooth analysis, convex analysis, and optimization, are provided that will help to make these fields accessible to a wider audience. In this paper, at first, we address some newly reported and interesting applications of multiobjective optimization in Management Science and Biology. Afterwards, some sufficient conditions for characterizing the feasible and improving directions of nonsmooth multiobjective optimization problems are given, and using these results a necessary optimality condition is proved. The sufficient optimality conditions are given utilizing a generalized convexity notion. Establishing necessary and sufficient optimality conditions for nonsmooth fractional programming problems is the next aim of the paper. We follow the paper by studying (strictly) prequasiinvexity and pseudoinvexity. Finally, some connections between these notions as well as some applications of these concepts in optimization are given.

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