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2010 Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization
Abdelkrim El Mouatasim
J. Appl. Math. 2010: 1-19 (2010). DOI: 10.1155/2010/976529


The random perturbation of generalized reduced gradient method for optimization under nonlinear differentiable constraints is proposed. Generally speaking, a particular iteration of this method proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phase, optimality is improved by means of the consideration of the objective function, on the tangent subspace to the constraints. In this paper, optimal assumptions are stated on the Restoration Phase and the Optimization Phase that establish the global convergence of the algorithm. Some numerical examples are also given by mixture problem and octagon problem.


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Abdelkrim El Mouatasim. "Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization." J. Appl. Math. 2010 1 - 19, 2010.


Published: 2010
First available in Project Euclid: 12 August 2011

zbMATH: 1206.90123
MathSciNet: MR2739749
Digital Object Identifier: 10.1155/2010/976529

Rights: Copyright © 2010 Hindawi

Vol.2010 • 2010
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