THE GENERALIZED REDUCED SUBGRADIENT ALGORITHM AS EXTENSION OF ABADIE GRG TO THE NONDIFFERENTIABLE CASE

Since the appearing of the reduced gradient method given by Wolfe, many authors have tried to obtain the convergence of this method or of a modified form if it (see e.g. Luenberger). This method is designed to solve a non-linear problem subject to linear equality and bound constraints, use the principle of the variables decomposition into basic and non-basic variables and the computation of the pivot as an extension of the simplex method. It has been generalized to non-linear equality constraints by application of the implicit function theorem, this generalization is called the generalized reduced gradient method: GRG due to Abadie and Carpentier. In this paper, we study the adaptation of the GRG to the non-differentiable case by using bundle techniques introduced by Lemarechal and applied to linear contraints by Bihain, Nguyen and Strodiot.