Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative

Chalco-Cano, Y.; Lodwick, Weldon A.; Rufián-Lizana, A.

doi:10.1007/s10700-013-9156-y

Cited by 117 publications

(84 citation statements)

References 33 publications

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“…Multiplying each inequality (16)(17)(18)(19)(20) by the corresponding Lagrange multiplier, we get, respectively,…”

Section: Definition 24mentioning

confidence: 99%

“…In [16], Hladık proposed a technique to determine the optimal bounds for nonlinear mathematical programming problems with interval data that ensures the exact bounds to enclose the set of all optimal solutions. Chalco-Cano et al [17] developed a method for solving the considered optimization problem with the interval-valued objective function considering order relationships between two closed intervals. Recently, Karmakar and Bhunia [18] proposed an alternative optimization technique for solving interval objective constrained optimization problems via multiobjective programming.…”

Section: Introductionmentioning

confidence: 99%

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Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Antczak

2017

J Optim Theory Appl

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In the paper, the classical exact absolute value function method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value penalty function method is analyzed under assumption that the functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value penalty function are given.Keywords Interval-valued optimization problem · Exact absolute value penalty function method · Penalized optimization problem with the interval-valued exact absolute value penalty function · Exactness of the exact absolute value penalty function method · LU-convex function Mathematics Subject Classification 49M30 · 90C25 · 90C30Communicated by

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“…Multiplying each inequality (16)(17)(18)(19)(20) by the corresponding Lagrange multiplier, we get, respectively,…”

Section: Definition 24mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Antczak

2017

J Optim Theory Appl

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“…Also, the gH-difference of two intervals A = [a, a] and B = b, b always exists and it is equal to (see Proposition 4 in [13]) The order relation was initially introduced in [10] and used in interval optimization problems, see [4,7,8,15,16].…”

Section: Definition 1 ([13]) the Generalized Hukuhara Difference Of Tmentioning

confidence: 99%

“…So, we follow a similar solution concept as that used in multiobjective programming problem to to define a minimum. In [1,4,5,9,14,15,16,17,18,19] the authors considered the following concept of minimum for interval-valued functions.…”

Section: Interval Optimization Problemsmentioning

confidence: 99%

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A note on optimality conditions to interval optimization problems

Chalco-Cano

Osuna-Gómez

Hernández‐Jiménez

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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In this article we examine to necessary and sufficient optimality conditions for interval optimization problems. We introduce a new concept of stationary point for an interval-valued function based on the gH-derivative. We show the importance the this concept from a practical and computational point of view. We introduce a new concept of invexity for gH-differentiable interval-valued function which generalizes previous concepts and we prove that it is a sufficient optimality condition. Finally, we show that the concepts of differentiability, convexity and invexity for interval-valued functions based on the differentiability, convexity and invexity of its endpoint functions are not adequate tools for interval optimization problems.

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