Solving continuous and discrete nonlinear programs with BARON

Under development since the early 1990s, BARON has become a highly robust and efficient computational system for solving nonconvex continuous and discrete optimization problems to global optimality. This work discusses key features that were introduced to BARON in the past decade, including hybrid relaxations, linear and nonlinear presolve methods, enhanced convexification methods, heuristics, and various robustness enhancements. A systematic computational comparison on benchmark libraries is presented among various state-of-the-art local and global codes for nonlinear and mixed-integer nonlinear programs. The results demonstrate the benefits from the newly added algorithmic facilities, and the leading performance of BARON over both local and global solvers.