A generalized proximal point algorithm for certain non-convex minimization problems

Abstract

An algorithm is presented for minimizing a function which is the sum of a continuously differentiable function and a convex function. The class of such problems contains as a special case that of minimizing a continuously differentiable function over a closed convex set. This algorithm may be viewed as a generalization of the proximal point algorithm to cope with non-convexity of the objective function by linearizing the differentiable term at each iteration. Convergence of the algorithm is proved and the rate of convergence is analysed.