Capabilities of Constraint Programming in Safe Global Optimization

We investigate the capabilities of constraints programming techniques in rigorous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron, and safe but slow global optimization approaches. We show how constraint programming filtering techniques can be used to implement optimality-based reduction in a safe and efficient way, and thus to take advantage of the known bounds of the objective function to reduce the domain of the variables, and to speed up the search of a global optimum. We describe an efficient strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equalities and inequalities to compute efficiently a promising upper bound. Experiments on the COCONUT benchmarks demonstrate that these different techniques drastically improve the performances.