A bundle method for nonsmooth DC programming with application to chance-constrained problems

Wim van Ackooij, Sophie Demassey, Paul Javal, Hugo Morais, Welington de Oliveira, Bhargav Swaminathan

Abstract: This work considers nonsmooth and nonconvex optimization problems whose objective and constraint functions are defined by difference-of-convex (DC) functions. We consider an infeasible bundle method based on the so-called improvement functions to compute critical points for problems of this class. Our algorithm neither employs penalization techniques nor solves subproblems with linearized constraints. The approach, which encompasses bundle methods for nonlinearly-constrained convex programs, defines trial points as solutions of strongly convex quadratic programs. Different stationarity definitions are investigated, depending on the functions’ structures. The approach is assessed in a class of nonsmooth DC-constrained optimization problems modeling chance-constrained programs.