PSwarm: A hybrid solver for linearly constrained global derivative-free optimization

Abstract

PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, the algorithm incorporated a particle swarm scheme for dissemination and thus it can globally explore the possible nonconvexity of the objective function. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods also based on function values. PSwarm is extended is this paper to handle general linear constraints. The poll step incorporates now positive generators for the tangent cone of the approximated active constraints, including a provision for the degenerate case. The search step has also been adapted accordingly. In particular, the initial population for particle swarm used in the search step is computed by first inscribing an ellipsoid of maximum volume to the feasible set. We have again compared PSwarm to other solvers (including some designed for global optimization) and the results confirm its competitiveness in terms of efficiency and robustness.