On multiple-cost optimization and extended controlled vector inequalities

Savin Treanţă; Marilena Ciontescu; Savin Treanţă; Marilena Ciontescu

doi:10.3934/era.2025313

Electronic Research Archive

2025, Volume 33, Issue 11: 7085-7102. doi: 10.3934/era.2025313

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Research article

On multiple-cost optimization and extended controlled vector inequalities

Savin Treanţă ^{1,2,3
,
,},
Marilena Ciontescu ¹

1.
Department of Applied Mathematics, National University of Science and Technology POLITEHNICA Bucharest, Bucharest 060042, Romania
2.
Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania
3.
Fundamental Sciences Applied in Engineering - Research Center (SFAI), National University of Science and Technology POLITEHNICA Bucharest, Bucharest 060042, Romania

Received: 21 August 2025 Revised: 12 November 2025 Accepted: 17 November 2025 Published: 21 November 2025

In this study, we established several relations between generalized (weak) vector controlled inequalities of Minty and Stampacchia type and the associated multi-cost models. To this end, we introduced the updated concepts of preconvexity and (strictly) strong convexity for functionals governed by controlled simple integrals and a mean-value-type result. Also, we introduced the corresponding multiobjective extremization models. The theoretical notions and the main results were justified by suitable numerical examples that were non-trivial.
- multiple-cost optimization,
- control inequalities,
- convexity,
- efficient point,
- preconvexity
Citation: Savin Treanţă, Marilena Ciontescu. On multiple-cost optimization and extended controlled vector inequalities[J]. Electronic Research Archive, 2025, 33(11): 7085-7102. doi: 10.3934/era.2025313

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Abstract

In this study, we established several relations between generalized (weak) vector controlled inequalities of Minty and Stampacchia type and the associated multi-cost models. To this end, we introduced the updated concepts of preconvexity and (strictly) strong convexity for functionals governed by controlled simple integrals and a mean-value-type result. Also, we introduced the corresponding multiobjective extremization models. The theoretical notions and the main results were justified by suitable numerical examples that were non-trivial.

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