scholarly journals Sufficient optimality conditions for semi-infinite multiobjective fractional programming under (Ф,ρ)-V-invexity and generalized (Ф,ρ)-V-invexity

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3649-3665 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Fundamental Property ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
New Class ◽  
Multiobjective Programming Problems

A new class of nonconvex smooth semi-infinite multiobjective fractional programming problems with both inequality and equality constraints is considered. We formulate and establish several parametric sufficient optimality conditions for efficient solutions in such nonconvex vector optimization problems under (?,?)-V-invexity and/or generalized (?,?)-V-invexity hypotheses. With the reference to the said functions, we extend some results of efficiency for a larger class of nonconvex smooth semi-infinite multiobjective programming problems in comparison to those ones previously established in the literature under other generalized convexity notions. Namely, we prove the sufficient optimality conditions for such nonconvex semi-infinite multiobjective fractional programming problems in which not all functions constituting them have the fundamental property of convexity, invexity and most generalized convexity notions.

scholarly journals Optimality and duality results for E-differentiable multiobjective fractional programming problems under E-convexity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tadeusz Antczak ◽  
Najeeb Abdulaleem
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
New Class ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Differentiable Functions ◽  
Optimality And Duality

Abstract A new class of (not necessarily differentiable) multiobjective fractional programming problems with E-differentiable functions is considered. The so-called parametric E-Karush–Kuhn–Tucker necessary optimality conditions and, under E-convexity hypotheses, sufficient E-optimality conditions are established for such nonsmooth vector optimization problems. Further, various duality models are formulated for the considered E-differentiable multiobjective fractional programming problems and several E-duality results are derived also under appropriate E-convexity hypotheses.

scholarly journals Nonsmooth Multiobjective Fractional Programming with Local Lipschitz ExponentialB-p,r-Invexity

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Shun-Chin Ho
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
Nonconvex Functions ◽  
Invex Functions ◽  
Multiobjective Fractional Programming Problem ◽  
Duality Model ◽  
Duality Problem

We study nonsmooth multiobjective fractional programming problem containing local Lipschitz exponentialB-p,r-invex functions with respect toηandb. We introduce a new concept of nonconvex functions, called exponentialB-p,r-invex functions. Base on the generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient solution. Furthermore, employing optimality conditions to perform Mond-Weir type duality model and prove the duality theorems including weak duality, strong duality, and strict converse duality theorem under exponentialB-p,r-invexity assumptions. Consequently, the optimal values of the primal problem and the Mond-Weir type duality problem have no duality gap under the framework of exponentialB-p,r-invexity.

scholarly journals Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR ◽  
2021 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Smooth Vector ◽  
Duality Results ◽  
Vanishing Constraints ◽  
Multiobjective Programming Problems

AbstractIn this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

scholarly journals On semi-G-V-type I concepts for directionally differentiable multiobjective programming problems

2016 ◽  
Vol 6 (2) ◽  
pp. 189-203
Author(s):  
Tadeusz Antczak ◽  
Gabriel Ruiz-Garzón
Keyword(s):  
Optimality Conditions ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Invex Functions ◽  
Differentiable Functions ◽  
Necessary And Sufficient ◽  
Multiobjective Programming Problems

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V-type I objective and constraint functions and their generalizations are introduced for such nonsmooth vector optimization problems. Based upon these generalized invex functions, necessary and sufficient optimality conditions are established for directionally differentiable multiobjective programming problems. Thus, new Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considered directionally differentiable multiobjective programming problem. Further, weak, strong and converse duality theorems are also derived for Mond-Weir type vector dual programs.

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.

New second-order radial epiderivatives and applications to optimality conditions

2020 ◽  
Vol 54 (4) ◽  
pp. 949-959
Author(s):  
Xiaoyan Zhang ◽  
Qilin Wang
Keyword(s):  
Optimality Conditions ◽  
Recent Literature ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Contingent Epiderivative ◽  
Proper Efficient Solutions

In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.

scholarly journals Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized(ℱ,b,ϕ,ρ,θ)-Univex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jen-Chwan Liu ◽  
Chun-Yu Liu
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Dual Model ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Optimality And Duality ◽  
Necessary And Sufficient

We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized(ℱ,b,ϕ,ρ,θ)-univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized(ℱ,b,ϕ,ρ,θ)-univex functions.

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