Exact l 1 penalty function for nonsmooth multiobjective interval-valued problems

Julie Khatri; Ashish Kumar Prasad

Kybernetika (2024)

  • Volume: 60, Issue: 5, page 652-681
  • ISSN: 0023-5954

Abstract

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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 ρ ) 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.

How to cite

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Khatri, Julie, and Prasad, Ashish Kumar. "Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems." Kybernetika 60.5 (2024): 652-681. <http://eudml.org/doc/299733>.

@article{Khatri2024,
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.},
author = {Khatri, Julie, Prasad, Ashish Kumar},
journal = {Kybernetika},
keywords = {interval-valued problem; multiobjective programming; exact l$_1$ penalty function; LU-efficient solution},
language = {eng},
number = {5},
pages = {652-681},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems},
url = {http://eudml.org/doc/299733},
volume = {60},
year = {2024},
}

TY - JOUR
AU - Khatri, Julie
AU - Prasad, Ashish Kumar
TI - Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
VL - 60
IS - 5
SP - 652
EP - 681
AB - 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.
LA - eng
KW - interval-valued problem; multiobjective programming; exact l$_1$ penalty function; LU-efficient solution
UR - http://eudml.org/doc/299733
ER -

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