scholarly journals Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

2021 ◽  
Vol 189 (1) ◽  
pp. 221-243
Author(s):  
Jiawei Chen ◽  
Suliman Al-Homidan ◽  
Qamrul Hasan Ansari ◽  
Jun Li ◽  
Yibing Lv
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Uncertain Data ◽  
Necessary Optimality Conditions

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 Minimax fractional programming with nondiferentiable (G,β)-invexity

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2027-2035 ◽  
Author(s):  
Xiaoling Liu ◽  
Dehui Yuan
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Dual Problem ◽  
Necessary Optimality Conditions ◽  
Minimax Programming ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Locally Lipschitz ◽  
Minimax Fractional Programming

In this paper, we consider the minimax fractional programming Problem (FP) in which the functions are locally Lipschitz (G,?)-invex. With the help of a useful auxiliary minimax programming problem, we obtain not only G-sufficient but also G-necessary optimality conditions theorems for the Problem (FP). With G-necessary optimality conditions and (G,?)-invexity in the hand, we further construct dual Problem (D) for the primal one (FP) and prove duality results between Problems (FP) and (D). These results extend several known results to a wider class of programs.

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.

A concept of inner prederivative for set-valued mappings and its applications

2018 ◽  
Vol 24 (3) ◽  
pp. 1059-1074
Author(s):  
Michel H. Geoffroy ◽  
Yvesner Marcelin
Keyword(s):  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Welfare Economics ◽  
Inverse Mapping ◽  
First Order ◽  
Inverse Mapping Theorem ◽  
Homogeneous Set ◽  
Optimal Allocations ◽  
Variational Perturbations ◽  
Set Valued Mappings

We introduce a class of positively homogeneous set-valued mappings, called inner prederivatives, serving as first order approximants to set-valued mappings. We prove an inverse mapping theorem involving such prederivatives and study their stability with respect to variational perturbations. Then, taking advantage of their properties we establish necessary optimality conditions for the existence of several kind of minimizers in set-valued optimization. As an application of these last results, we consider the problem of finding optimal allocations in welfare economics. Finally, to emphasize the interest of our approach, we compare the notion of inner prederivative to the related concepts of set-valued differentiation commonly used in the literature.

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