Stochastic geometric optimization with joint probabilistic constraints

This paper discusses geometric programs with joint probabilistic constraints. When the stochastic parameters are normally distributed and independent of each other, we approximate the problem by using piecewise linear functions, and transform the approximation problem into a convex geometric program. We prove that this approximation method provides a lower bound. Then, we design a sequential convex optimization algorithm to find an upper bound. Finally, numerical tests are carried out on a stochastic shape optimization problem.