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A hybrid algorithm for nonlinear equality constrained optimization problems: global and local convergence theory

Mohammedi El Hallabi (hallabi_medi***at***yahoo.fr)

Abstract: In this paper we combine both trust-region and linesearch globalization strategies in a globally convergent hybrid algorithm to solve a continuously differentiable nonlinear equality constrained minimization problem. First, the trust-region approach is used to determine a descent direction of the augmented Lagrangian chosen as the merit function, and second, linesearch techniques are used to obtain an acceptable steplength in such a direction. Under rather weak hypotheses and without the usual regularity assumption that the linearized constraints gradients are linearly independent, we prove that the hybrid algorithm is globally convergent. Moreover, under the standard hypotheses of the SQP method, we prove that the rate of convergence is q-quadratic. Some numerical results are given in comparaison with the pure trust-region strategy.

Keywords: Cauchy Decrease, Constrained Optimization, Equality Constrained, Global Convergence, Negative Curvature, Non Regularity, Quadratic Convergence, Trust-Region.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Robust Optimization

Citation: unpublished. Technical Report TR4-99. Mathematics and Computer Science Depart. Institut National des Postes et Telecommunications. April, 1999.

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Entry Submitted: 04/03/2003
Entry Accepted: 04/03/2003
Entry Last Modified: 04/29/2014

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