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A simplicial homology interior-point algorithm for nonlinear programming | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 اردیبهشت 1405 اصل مقاله (410.32 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30665.2567 | ||
| نویسندگان | ||
| Ayat Ababneh؛ Baha Alzalg* | ||
| Department of Mathematics, The University of Jordan, Amman, Jordan | ||
| چکیده | ||
| In this paper, we investigate the use of computational algebraic topology and simplicial homology within the framework of Sperner’s lemma to solve box- and inequality-constrained nonlinear (nonconvex) programming problems. The homology clustering method we consider provides optimal or near-optimal candidate solutions of locally convex subdomains in the search space by estimating the homology groups of a complex constructed on a hypersurface that is homeomorphic to a complex on the objective function. Each candidate point is then chosen as a starting point for a local iterative interior-point optimization technique that performs well on the corresponding locally convex subdomain. The best solution obtained from executing parallel interior-point techniques is the global optimal solution of the problem over the nonconvex domain. In addition, we compare the proposed method with the existing topographical interior-point approach and other solvers across various test problems. The computational results demonstrate that the simplicial interior-point algorithm performs well in finding the global minimum and outperforms both the topographical interior-point algorithm and the MIDACO solver in practice. | ||
| کلیدواژهها | ||
| Methods of algebraic topology؛ Simplicial homology؛ Nonlinear programming؛ Interior-point methods | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 28 تعداد دریافت فایل اصل مقاله: 23 |
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