Sequential Piecewise Linear Programming for Convergent Optimization of Non-Convex Problems

Abstract: A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although feasibility and optimality are not guaranteed, we show that the method is capable of obtaining convergent and optimal solutions on a number of Nonlinear Programming (NLP) and Mixed Integer Nonlinear Programming (MINLP) problems using only a small number of breakpoints and integer variables.