Quasi-Optimization Problems: Existence, Iterative Algorithms and Well-Posedness

Shengda Zeng (), Qing Nie () and Calogero Vetro ()
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Shengda Zeng: Chongqing Normal University
Qing Nie: Chongqing Jiaotong University
Calogero Vetro: Department of Mathematics and Computer Science

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 22, 21 pages

Abstract: Abstract The aim of this article is to introduce and study a quasi-optimization problem (QOP, for short) on an infinite dimensional Banach space. First, under mild assumptions, we deliver three existence theorems for (QOP) by employing Kluge’s fixed point principle for multivalued operators. Then, several sufficient and necessary conditions for a solution of (QOP) are proved. Furthermore, two iterative algorithms are proposed and the convergence results are obtained. Finally, the well-posedness and generalized well-posedness of (QOP) are introduced and its equivalent metric characteristic is established.

Keywords: Quasi-optimization problem; Existence; Well-posedness; Iterative algorithm; Sufficient and necessary condition; 49J53; 49K99 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02701-9

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