A Gauss-Newton Approach for Solving Constrained Optimization Problems Using Differentiable Exact Penalties

被引:5
作者
Andreani, Roberto [1 ]
Fukuda, Ellen H. [1 ]
Silva, Paulo J. S. [2 ]
机构
[1] Univ Estadual Campinas, Dept Appl Math, IMECC, Campinas, Brazil
[2] Univ Sao Paulo, Dept Comp Sci, IME, Sao Paulo, Brazil
基金
巴西圣保罗研究基金会;
关键词
Exact penalty; Multipliers estimate; Nonlinear programming; Semismooth Newton method; NONLINEAR-PROGRAMMING PROBLEMS; AUGMENTED LAGRANGIAN FUNCTION; GLOBAL CONVERGENCE PROPERTIES; INEQUALITY CONSTRAINTS; ALGORITHM; DUALITY; SQP;
D O I
10.1007/s10957-012-0114-6
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We propose a Gauss-Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by Andre and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of the KKT conditions as a system of equations. Such reformulation allows the use of a semismooth Newton method, so that local superlinear convergence rate can be proved under an assumption weaker than the usual strong second-order sufficient condition and without requiring strict complementarity. Besides, we note that the exact penalty function can be used to globalize the method. We conclude with some numerical experiments using the collection of test problems CUTE.
引用
收藏
页码:417 / 449
页数:33
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