The $ F $-objective function method for differentiable interval-valued vector optimization problems

Tadeusz Antczak

doi:10.3934/jimo.2020093

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2021, Volume 17, Issue 5: 2761-2782. Doi: 10.3934/jimo.2020093

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The $ F $-objective function method for differentiable interval-valued vector optimization problems

Tadeusz Antczak

Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Received: June 30, 2019

Revised: December 31, 2019

Early access: May 2020

Published: September 2021

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In this paper, a differentiable vector optimization problem with the multiple interval-valued objective function and with both inequality and equality constraints is considered. The Karush-Kuhn-Tucker necessary optimality conditions are established for such a differentiable interval-valued multiobjective programming problem. Further, a new approach, called $ F $-objective function method, is introduced for solving the considered differentiable vector optimization problem with the multiple interval-valued objective function. In this method, its associated vector optimization problem with the multiple interval-valued $ F $-objective function is constructed. Their equivalence is established under $ F $-convexity assumptions. It is shown that the introduced approach can be used to solve a nonlinear nonconvex interval-valued optimization problem. By using the introduced approximation method, it is also presented in some cases that a nonlinear nonconvex interval-valued optimization problem can be solved by the help of methods for solving linear interval-valued optimization problems.

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Mathematics Subject Classification: 90C29, 90C30, 90C46, 90C59, 90C26.

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