Optimality conditions associated with new controlled extremization models

Tareq Saeed; Tareq Saeed

doi:10.3934/math.2024842

AIMS Mathematics

2024, Volume 9, Issue 7: 17319-17338. doi: 10.3934/math.2024842

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Research article

Optimality conditions associated with new controlled extremization models

Tareq Saeed ^,

Financial Mathematics and Actuarial Science (FMAS)- Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, 21589-Jeddah, Saudi Arabia

Received: 13 March 2024 Revised: 14 April 2024 Accepted: 28 April 2024 Published: 20 May 2024
MSC : 26B25, 49J20, 90C17, 90C32, 90C46

Applying a parametric approach, in this paper we studied a new class of multidimensional extremization models with data uncertainty. Concretely, first, we derived the robust conditions of necessary optimality. Thereafter, we established robust sufficient optimality conditions by employing the various forms of convexity of the considered functionals. In addition, we formulated an illustrative example to validate the theoretical results.
- optimization problem,
- robust optimal solution,
- convexity,
- concavity,
- necessary and sufficient conditions of optimality
Citation: Tareq Saeed. Optimality conditions associated with new controlled extremization models[J]. AIMS Mathematics, 2024, 9(7): 17319-17338. doi: 10.3934/math.2024842

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Abstract

Applying a parametric approach, in this paper we studied a new class of multidimensional extremization models with data uncertainty. Concretely, first, we derived the robust conditions of necessary optimality. Thereafter, we established robust sufficient optimality conditions by employing the various forms of convexity of the considered functionals. In addition, we formulated an illustrative example to validate the theoretical results.

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