.png){kind=icon}
返回
IMPLEMENTING A SMOOTH EXACT PENALTY FUNCTION FOR GENERAL CONSTRAINED NONLINEAR OPTIMIZATION
.png){kind=icon}
OA
AI
DOI：10.1137/19M1255069.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We build upon R. Estrin et al., [SIAM J. Sci. Comput., 42 (2020), pp. A1809-A1835] to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by R. Fletcher [Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, (1970), pp. 157-175; Math. Program., 5 (1973), pp. 129-150]. Although Fletcher's approach has historically been considered impractical, we show that the computational kernels required are no more expensive than those in other widely accepted methods for nonlinear optimization. The main kernel for evaluating the penalty function and its derivatives solves structured linear systems. When the matrices are available explicitly, we store a single factorization each iteration. Otherwise, we obtain a factorization-free optimization algorithm by solving each linear system iteratively. The penalty function shows promise in cases where the linear systems can be solved efficiently, e.g., PDE-constrained optimization problems when efficient preconditioners exist. We demonstrate the merits of the approach, and give numerical results on several PDE-constrained and standard test problems.
Keyword:
nonlinear programming
exact penalty
smooth penalty
factorization free
iterative methods
trust region
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
机构
引用论文
.png){kind=icon}
分享收藏分享收藏
查看更多内容