Kybernetika 60 no. 5, 652-681, 2024

Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems

Julie Khatri and Ashish Kumar PrasadDOI: 10.14736/kyb-2024-5-0652

Abstract:

Our objective in this article is to explore the idea of an unconstrained problem using the exact l$_1$ penalty function for the nonsmooth multiobjective interval-valued problem (MIVP) having inequality and equality constraints. First of all, we figure out the KKT-type optimality conditions for the problem (MIVP). Next, we establish the equivalence between the set of weak LU-efficient solutions to the problem (MIVP) and the penalized problem (MIVP$_\rho$) with the exact l$_1$ penalty function. The utility of this transformation lies in the fact that it converts constrained problems to unconstrained ones. To accurately predict the applicability of the results presented in the paper, meticulously crafted examples are provided.

Keywords:

interval-valued problem, multiobjective programming, exact l$_1$ penalty function, LU-efficient solution

Classification:

49J52, 49M30, 90C29, 90C46

paper.pdf

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