Penalty approach for KT-pseudoinvex multidimensional variational control problems-Reference-Cited by-同舟云学术

Penalty approach for KT-pseudoinvex multidimensional variational control problems

Published:2022 Issue:3 Volume:8 Page:5687-5702
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Preeti ¹,Agarwal Poonam²,Treanţă Savin³⁴⁵,Nonlaopon Kamsing⁶

Affiliation:

1. Department of Mathematics-SAS, VIT Vellore, Vellore, Tamil Nadu, India

2. Department of Applied Science and Humanities, Inderprastha Engineering College, Ghaziabad, U.P, India

3. Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania

4. Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania

5. "Fundamental Sciences Applied in Engineering" Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania

6. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

<abstract><p>The present paper is the result of a contemplative study of a multi-time control problem (MCP) by considering its associated equivalent auxiliary control problem (MCP)$ _{\varsigma} $ via the exact $ l_{1} $ penalty method. Further study reveals that the solution set of the considered problem and the auxiliary problem exhibits an equivalence under the KT-pseudoinvexity hypothesis. Moreover, the study is extended towards the saddle point defined for (MCP) to establish the relationship between the solution set of multi-time control problem (MCP) and its associated equivalent auxiliary control problem (MCP)$ _{\varsigma} $. Finally, we present an illustrative application to authenticate the results presented in this paper.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference21 articles.

1. M. Arana-Jim$\acute{e}$nez, G. Ruiz-Garz$\acute{o}$n, A. Rufi$\acute{a}$n-Lizana, R. Osuna-G$\acute{o}$mez, Weak efficiency in multiobjective variational problems under generalized convexity, J. Global Optim., 52 (2012), 109–121. https://doi.org/10.1007/s10898-011-9689-y

2. T. Antczak, Exact penalty function method for mathematical programming problems involving invex functions, Eur. J. Oper. Res., 198 (2009), 29–36. https://doi.org/10.1016/j.ejor.2008.07.031

3. T. Antczak, The $l_{1}$ penalty function method for nonconvex differentiable optimization problems with inequality constraints, Asia-Pac. J. Oper. Res., 27 (2010), 1–18. https://doi.org/10.1142/S0217595910002855

4. T. Antczak, The exact $l_{1}$ penalty function method for nonsmooth invex optimization problems, System Modelling and Optimization, 25th IFIP TC 7 Conference, CSMO 2011 Berlin, Germany, 2011.

5. I. I. Eremin, The penalty method in convex programming, Doklady Akad. Nauk SSSR, 143 (1967), 748–751. https://doi.org/10.1007/BF01071708