Interior proximal methods for quasiconvex optimization

A generalized proximal point algorithm for the minimization of a nonconvex function on a feasible set is investigated. It is known that if the objective function of the given problem is (lower semicontinuous, proper and) convex, well‐definedness of the method as well as convergence of the generated iterates, being the solutions of better conditioned and uniquely solvable subproblems, are known. The present paper contributes to the discussion of the methods’ behaviour when the objective is not convex. This gives rise to questions, among others, of well‐definedness and convergence of the generated sequence.