Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization | Zendy

Abdelkrim El Mouatasim | Zendy

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Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization

Author(s) -

Abdelkrim El Mouatasim

Publication year - 2010

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2010/976529

Subject(s) - mathematics , differentiable function , mathematical optimization , perturbation (astronomy) , subspace topology , nonlinear system , convergence (economics) , tangent cone , nonlinear programming , optimization problem , tangent , global optimization , gradient method , phase (matter) , mathematical analysis , chemistry , physics , geometry , organic chemistry , quantum mechanics , economics , economic growth

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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