| Autor: |
Lee, Jae Hyoung, Lee, Gue Myung, Pham, Tien Son |
| Rok vydání: |
2023 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
Consider the problem of minimizing a lower semi-continuous semi-algebraic function $f \colon \mathbb{R}^n \to \mathbb{R} \cup \{+\infty\}$ on an unbounded closed semi-algebraic set $S \subset \mathbb{R}^n.$ Employing adequate tools of semi-algebraic geometry, we first establish some properties of the tangency variety of the restriction of $f$ on $S.$ Then we derive verifiable necessary and sufficient conditions for the existence of optimal solutions of the problem as well as the boundedness from below and coercivity of the restriction of $f$ on $S.$ We also present a computable formula for the optimal value of the problem. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
