An outcome space branch and bound algorithm for affine multiplicative problems using piecewise linear approximation technique

This paper presents an efficient algorithm for solving a class of affine multiplication programs(AMP). In order to obtain the global optimal solution of the problem, we first transform the problem into an equivalent problem by introducing auxiliary variables. Secondly, we utilize a new piecewise linear approximation technology to systematically transform the problem into a series of linear relaxation programming problems to obtain a reliable lower bound of the optimal value of the problem. Hence, according to the characteristics of the problem and the structure of the branch-and-bound framework, some outer space acceleration techniques are constructed to improve the convergence speed of the algorithm. In addition, by analyzing the computational complexity of the algorithm, an estimate of the maximum number of iterations of the algorithm is given. Finally, numerical results verify the effectiveness and robustness of the algorithm.