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April  2013, 9(2): 391-409. doi: 10.3934/jimo.2013.9.391

## A penalty-free method for equality constrained optimization

 1 School of Mathematics Science, Soochow University, Suzhou, 215006, China, China, China

Received  September 2011 Revised  January 2013 Published  February 2013

A penalty-free method is introduced for solving nonlinear programming with nonlinear equality constraints. This method does not use any penalty function, nor a filter. It uses trust region technique to compute trial steps. By comparing the measures of feasibility and optimality, the algorithm either tries to reduce the value of objective function by solving a normal subproblem and a tangential subproblem or tries to improve feasibility by solving a normal subproblem only. In order to guarantee global convergence, the measure of constraint violation in each iteration is required not to exceed a progressively decreasing limit. Under usual assumptions, we prove that the given algorithm is globally convergent to first order stationary points. Preliminary numerical results on CUTEr problems are reported.
Citation: Zhongwen Chen, Songqiang Qiu, Yujie Jiao. A penalty-free method for equality constrained optimization. Journal of Industrial & Management Optimization, 2013, 9 (2) : 391-409. doi: 10.3934/jimo.2013.9.391
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