Generalized Polyhedral DC Optimization Problems
Optimization and Control
2024-12-02 v1
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.
Cite
@article{arxiv.2411.19272,
title = {Generalized Polyhedral DC Optimization Problems},
author = {Vu Thi Huong and Duong Thi Kim Huyen and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:2411.19272},
year = {2024}
}