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A penalty-free method for equality constrained optimization

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  • 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.
    Mathematics Subject Classification: Primary: 65K05; Secondary: 90C26, 90C30.

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