A Sequential Linear Programming Algorithm for Continuous and Mixed-Integer Nonconvex Quadratic Programming

Abstract

In this work, we propose a new approach called “Sequential Linear Programming (SLP) algorithm” for finding an approximate global minimum of continuous and mixed-integer nonconvex quadratic programs (qps). In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and we presented some numerical experiments which compare the performance of our algorithm with the branch and cut algorithm implemented in CPLEX12.8 on 28 concave quadratic test problems, 64 nonconvex quadratic test problems and 12 mixed-integer nonconvex qps. The numerical results show that our algorithm has successfully found similar global objective values as CPLEX12.8 in almost all the considered test problems and it is competitive with CPLEX12.8, particularly in solving large problems (number of variables greater that 50 and less than 1000).