Optimality conditions for nonsmooth multiobjective bilevel optimization problems

Chương, Thái Doãn

doi:10.1007/s10479-017-2734-6

Cited by 18 publications

(2 citation statements)

References 36 publications

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“…Zimmerman [30] proposed an approach for solving multi-objective optimization problem using fuzzy programming. Optimality conditions for non-smooth multi-objective bi-level problems were discussed by TD Chuong in 2020 in [31]. Gandhi et al in [32] discussed the optimality conditions for multiobjective bi-level optimization problem involving set valued constraints.…”

Section: Literature Reviewmentioning

confidence: 99%

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

Singh

Sharma

Chakraborty

et al. 2022

Complex Intell. Syst.

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This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper.

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Section: Literature Reviewmentioning

confidence: 99%

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

Singh

Sharma

Chakraborty

et al. 2022

Complex Intell. Syst.

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“…The modeling of problems as (P) covers broad classes of various optimization problems such as conic vector optimization problems, (standard) multiobjective/vector optimization problems, multiobjective approximation problems [8,23,42], and many optimization problems manufactured in practical fields like engineering or economics and finance, Over the last couple of decades, issues related to optimality conditions and duality for (weakly) efficient solutions of the model problem (P) have been extensively investigated in the literature; see [1,2,7,8,23,31,32,36] and other references therein. For other results concerning on optimality conditions and duality in both smooth/nonsmooth multiobjective/vector optimization problems involving convex/generalized convex functions, we refer the readers to [3,5,6,24,25,38,41] and other references therein.…”

Section: Introductionmentioning

confidence: 99%

Approximate optimality and approximate duality in nonsmooth composite vector optimization

Sirichunwijit¹,

Wangkeeree²,

Sisarat³

2021

CJM

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This paper concentrates on studying a nonsmooth composite vector optimization problem (P for brevity). We employ a fuzzy necessary condition for approximate (weakly) efficient solutions of a nonconvex and nonsmooth cone constrained vector optimization problem established in [Choung, T. D. Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization Ann. Oper. Res. (2020), https://doi.org/10.1007/s10479-020-03740-3.] and the a chain rule for generalized differentiation to provide a necessary condition which exhibited in a Fritz-John type for approximate (weakly) efficient solutions of P. Sufficient optimality conditions for approximate (weakly) efficient solutions to P are also provided by means of proposing the use of (strictly) approximately generalized convex composite vector functions with respect to a cone. Moreover, an approximate dual vector problem to P is given and strong and converse duality assertions for approximate (weakly) efficient solutions are proved.

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A Concise Review on Recent Optimization and Deep Learning Applications in Blockchain Technology

Ganesan

Elamvazuthi

Vasant

et al. 2022

Artificial Intelligence in Industry 4.0 and 5G Technology

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Optimality conditions for nonsmooth multiobjective bilevel optimization problems

Cited by 18 publications

References 36 publications

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

Approximate optimality and approximate duality in nonsmooth composite vector optimization

A Concise Review on Recent Optimization and Deep Learning Applications in Blockchain Technology

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