Sequential Global Linear Programming Algorithm for Continuous Piecewise Linear Programming

This paper works on a descent algorithm for continuous piecewise linear (CPWL) minimization problems. CPWL minimization is a widely applied nonlinear programming, which can be equivalently transformed into a difference of convex functions (DC) programming, and then, a concave optimization over a polyhedron. By utilizing the concavity of the objective function, the sequential global linear programming (SGLP) algorithm is proposed. The SGLP algorithm makes use of global information of the polyhedral feasible domain to gain superior optimizing capacity, while applies the mature linear programming technique to insure a rapid algorithm speed. In the numerical experiments, SGLP is compared with two other algorithms of DCA and DALPT, and shows its superior optimization efficiency.