Comparison of Algorithms for Including Equality Constraints in Signomial Programming ACDL Technical Report TR-2017-1

Including equality constraints in signomial programming proves troublesome, because a straightforward difference of convex formulation for such a constraint results in a singular point. Signomial programs are usually solved by solving successive geometric programs, and the focus of this paper is on methods for approximating equality constraints in signomial programs as geometric programs. A general comparison between convergence characteristics of such methods is presented here, focusing on local approaches to signomial programming. The introduced methods locally approximate equality constraints as inequalities and Taylor approximations, and are compared to a recently developed algorithm from the literature, which claims to achieve global optimality for these types of problems. Trust region methods are proposed which perform comparably well to an algorithm from the literature yet are numerically much simpler to implement. Finally, one of these methods is used to solve a design problem for a solar unmanned aerial vehicle.