Global optimization of signomial geometric programming using linear relaxation

Various local optimization approaches have been developed for solving signomial geometric programming (SGP) problems. But up to now, less work has been devoted to solving global optimization of SGP due to the inherent difficulty. This paper considers the global minimum of SGP that arises in various practice problems. By utilizing an exponential variable transformation and tangential hypersurfaces and convex envelope approximations a linear relaxation of SGP is then obtained. Thus initial nonconvex nonlinear problem SGP is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function. The proposed algorithm is convergent to the global minimum of SGP by means of the subsequent solutions of a series of linear programming problems. Test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of SGP on a microcomputer.