A Scalable Global Optimization Algorithm for Stochastic Nonlinear Programs

We propose a global optimization algorithm for stochastic nonlinear programs that uses a specialized spatial branch and bound (BB) strategy to exploit the nearly decomposable structure of the problem. In particular, at each node in the BB scheme, a lower bound is constructed by relaxing the so-called non-anticipativity constraints and an upper bound is constructed by fixing the first-stage variables to the current candidate solution. A key advantage of this approach is that both lower and upper bounds can be computed by solving individual scenario subproblems. Another key property of this approach is that we only need to perform branching on the first-stage variables to guarantee convergence (branching on the second-stage variables is performed implicitly during the computation of lower and upper bounds). The algorithm is implemented in SNGO in Julia and is interfaced to the modeling languages JuMP and Plasmo. Our implementation contains typical algorithmic features of global optimization solvers such as convexification, outer approximation, feasibility-based bound tightening, optimality-based bound tightening, and local search. Numerical experiments are performed using a stochastic optimization formulation for controller tuning, a parameter estimation formulation for microbial growth models, and a stochastic test set from GLOBALlib. We compare the computational results against SCIP and demonstrate that the new approach achieves significant speedups.