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El Mouatasim, Abdelkrim

Two-phase generalized reduced gradient method for constrained global optimization. (English) Zbl 1206.90123

J. Appl. Math. 2010, Article ID 976529, 19 p. (2010).
Summary: 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.

MSC:

90C26 Nonconvex programming, global optimization
90C52 Methods of reduced gradient type

Keywords:

random perturbation; restoration phase; optimization phase

Software:

simannf90
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\textit{A. El Mouatasim}, J. Appl. Math. 2010, Article ID 976529, 19 p.. (2010; Zbl 1206.90123)
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References:

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