An outer space branch-reduction-bound algorithm using second-order cone relaxation with regional reduction strategy for solving equivalent generalized linear multiplicative programming

Abstract

This paper proposes an outer space branch-reduction-bound algorithm by using the second-order cone relaxation technique with regional reduction strategy for solving generalized linear multiplicative programming (GLMP) problems. Firstly, by introducing additional variables and performing several equivalent transformations, the GLMP problem is converted into an equivalent problem that is easier to solve. Next, the non-convex quadratic constraint in the equivalent problem is handled utilizing the secant approximation method to formulate the second-order cone relaxation problem. Subsequently, we incorporate a regional reduction technique into the algorithm to enhance its computational performance and estimate the worst-case computational complexity, ensuring the attainment of the global optimal solution. Finally, numerical experimental results demonstrate that the proposed algorithm can efficiently search for the global $ϵ$-optimal solution of the test examples and can successfully solve high-dimensional GLMP problems with a small number of linear functions.