cGOP

cGOP is a package for rigorously solving nonconvex optimization problems to global optimality. The package implements the GOP algorithm (Floudas and Visweswaran, 1993), which is applicable to general constrained biconvex problems, using a set of C subroutines to solve these problems using decomposition and branch-and-bound techniques. It also incorporates several improvements made to the original GOP algorithm to reduce the computational complexity (Visweswaran and Floudas, 1993), as well as new formulations that permit implicit solutions of some of the subproblems encountered during the algorithmic steps (Visweswaran and Floudas, 1995). The algorithms use local optimization solvers (currently MINOS (Murtagh and Saunders, 1988) and CPLEX (CPLEX, 1995)) to solve linear, mixed-integer linear and convex subproblems. This version of the cGOP package can be used to solve problems with linear constraints. The original algorithm and its variants can be accessed by calls to high-level subroutines as well as through a standalone mode for quadratic problems. Furthermore, it can also be accessed using a high-level interface that permits easy description of the problems. The package has been in use at the Computer-Aided Systems Laboratory in Princeton University for the last two years, and has been used to solve problems involving several hundred variables and constraints.