Geodesic
Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems
Kybernetika, Tome 60 (2024) no. 5, pp. 652-681 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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$_\rho$) 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.
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.
DOI : 10.14736/kyb-2024-5-0652
Classification : 49J52, 49M30, 90C29, 90C46
Keywords: interval-valued problem; multiobjective programming; exact l$_1$ penalty function; LU-efficient solution 
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     author = {Khatri, Julie and Prasad, Ashish Kumar},
     title = {Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems},
     journal = {Kybernetika},
     pages = {652--681},
     year = {2024},
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     number = {5},
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Khatri, Julie; Prasad, Ashish Kumar. Exact l$_1$ penalty function for nonsmooth multiobjective interval-valued problems. Kybernetika, Tome 60 (2024) no. 5, pp. 652-681. doi: 10.14736/kyb-2024-5-0652

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