A NONLINEAR FEASIBILITY PROBLEM HEURISTIC

In this work we consider a region S ⊂ x ⁰ is given, which is close in certain norm to the analytic center of S, and that a new nonlinear smooth convex inequality is added to those defining S (perturbed region). It is constructively shown how to obtain a shift of the right-hand side of this inequality such that the point x ⁰ is still close (in the same norm) to the analytic center of this shifted region. Starting from this point and using the theoretical results shown, we develop a heuristic that allows us to obtain the approximate analytic center of the perturbed region. Then, we present a procedure to solve the problem of nonlinear feasibility. The procedure was implemented and we performed some numerical tests for the quadratic (random) case.

given by a finite number of nonlinear smooth convex inequalities and having nonempty interior. We assume a point

interior point; analytic center; convex optimization