Optimization Problems with Cone Constraints in Groups and Semigroups: An Approach Based on Image Space Analysis

Jun Li () and Giandomenico Mastroeni ()
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Jun Li: China West Normal University
Giandomenico Mastroeni: University of Pisa

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 3, No 8, 973-1007

Abstract: Abstract In this paper, a class of optimization problems with cone constraints in groups and semigroups is investigated by exploiting the image space analysis. Optimality is proved by means of separation arguments in the image space associated with the given problem, which turns out to be equivalent to the existence of saddle points of generalized Lagrangian functions under suitable assumptions. In particular, Lagrangian-type sufficient or necessary optimality conditions are obtained by introducing convex-like functions and using separation theorems between convex sets in groups and semigroups obtained by Li and Mastroeni.

Keywords: Image space analysis; Convex-like functions; Groups and semigroups; Separation; Optimization problems; 46N10; 90C48 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02161-z

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