Investigation of path-following algorithms for signomial geometric programming problems

This paper considers signomial geometric programming (GP) dual problems, a class of nonconvex nonlinear programming problems possessing multiple locally optimal solutions. The primary purpose of this paper is to investigate the quality of solutions found by use of a path-following algorithm. The path-following method may be applied to either the original nonconvex problem, or to each of a sequence of convex posynomial GP problems approximating the original problem. For each test problem, the algorithms were initiated with thousands of different starting points. It was determined that, when the stopping criterion was relaxed for early posynomial GP problems in the sequence, the ultimate solution tended to be of better quality, and more frequently globally optimal.