Pseudopower expansion of solutions of generalized equations and constrained optimization problems
Résumé
We compute the solution of a strongly regular perturbed generalized equations as the sum of a speudopower expansion, i.e. the expansion at order k is the solution of the generalized equation expanded at order k and thus depends itself on the perturbation parameter [??]. In the polyhedral case, the pseudopower expansion reduces to a classical Taylor expansion. For constrained optimization problems with strongly regular solution, we check that the quadratic growth condition holds and that, at least locally, solutions of the problem and solutions of the associated optimality system coincide. In the special case of a finite number of inequality constraints, the solution and the Lagrange multiplier can be expanded in Taylor series if the gradients of the active constraints are linearly independent. If the data are analytic, the solution and the multiplier are analytic functions in [??] provided that some strong second order condition holds.