Generalized Polyhedral DC Optimization Problems

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 207; no. 1; p. 11
Main Authors: Huong, Vu Thi, Kim Huyen, Duong Thi, Yen, Nguyen Dong
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.10.2025
Subjects:
Algorithms
Convex analysis
Convexity
Linear programming
Optimization
Theorems
Vector space
Vector spaces
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02769-3