Solving Non Separable Convex

Résumé: The aim of this paper is to present a new method for solving non-separable quadratic problems. In a first step we transform the non-separable quadratic problem in a separable quadratic problem equivalent. In a second step we solve the quadratic problem separable by the method of projection. The principle of this method is to calculate the critical point, if it is a feasible solution then this is the optimal solution. Otherwise, we construct a new feasible set by a homographic transformation on which we project the transformed critical point and we give the optimal solution belonging to the feasible set of the original problem. Note that the resolution is done directly on the primal separable quadratic problem and not on the linear problem as do several methods. The method is purely analytical and avoids the thorny problem of the choice of the initial solution.

Publié dans la revue: Models & Optimisation and Mathematical Analysis Journal