Generalized Polyhedral DC Optimization Problems

Vu Thi Huong (), Duong Thi Kim Huyen () and Nguyen Dong Yen ()
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Vu Thi Huong: Vietnam Academy of Science and Technology
Duong Thi Kim Huyen: Phenikaa University
Nguyen Dong Yen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 11, 28 pages

Abstract: Abstract The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the objective function is a generalized polyhedral convex function or the first component of the objective function is a generalized polyhedral convex function and the constraint set is generalized polyhedral convex. Various results on optimality conditions, the local solution set, the global solution set, and solution algorithms via duality are obtained. Useful illustrative examples are considered.

Keywords: Difference of convex functions; Generalized polyhedral convex function; Generalized polyhedral convex set; Optimality condition; Local solution set; Global solution set; DCA scheme; 91A05; 91A10; 90C05; 49J53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02769-3

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