Compact Estimation and Optimization of Signomial Geometric Programming

Among the broad class of non-linear programming, signomial geometric programming (SGP) still remains challenging in global optimization due to its non-convexity. The general framework of handling SGP problems is to approximate the SPG problems and solve a series of surrogate problems to approach its global optima. However, most of the methods in the literature requires integer variables and/or additional constraints, which burdens the solving procedures and leads to less efficiency. In this paper, we propose two compact surrogate models which underestimate and overestimate SGP problems, respectively. Moreover, the novel surrogate models consist of only continuous variables, requires no additional constraints, and have been proved to provide tight upper and lower bounds for the SGP problem with proper parameter configuration. In order to solve the proposed surrogate problems, we propose a global search algorithm which an enhanced local search procedures. In order to confirm the validity of the proposed model and the efficiency of the corresponding algorithm, we perform numerical experiments on both benchmark problems and the real-world application on designing sparse finite impulse filter (FIR) filters with comparison to some state-of-the-art algorithms.