Implementing a Smooth Exact Penalty Function for General Constrained Nonlinear Optimization
| Autor: | Ron Estrin, Michael P. Friedlander, Dominique Orban, Michael A. Saunders |
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| Rok vydání: | 2020 |
| Předmět: |
Computational Mathematics
021103 operations research Optimization and Control (math.OC) Applied Mathematics FOS: Mathematics 0211 other engineering and technologies Numerical Analysis (math.NA) Mathematics - Numerical Analysis 010103 numerical & computational mathematics 02 engineering and technology 0101 mathematics Mathematics - Optimization and Control 01 natural sciences |
| Zdroj: | SIAM Journal on Scientific Computing. 42:A1836-A1859 |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/19m1255069 |
| Popis: | We build upon Estrin et al. (2019) to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970, 1973b). 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. 25 pages. arXiv admin note: text overlap with arXiv:1910.04300 |
| Databáze: | OpenAIRE |
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