Large-scale nonlinear programming algorithm using projection methods (Q2717932)

This paper is aimed at presenting a study how projection methods (for feasibility problems) can be used in decomposing large scale nonlinear optimization problems: the original optimization problem is reduced to a sequence of feasibility problems, i.e. problems of finding a common point of several sets. The feasibility problem is solved by making sequential projections onto two sets: one ``linear'' (defined by linear constraints) and one ``nonlinear'' (defined by nonlinear constraints).NEWLINENEWLINENEWLINEAn important feature of the described approach is that there is no need to add accelerating cuts after each projection. The construction of the method is based on zigzagging phenomenon and provides a nonasymptotic convergence. The method and its variants are described in detail. The convergence analysis and results of experimentation, as well as possible extensions are given.