Project : coprin
Section: New Results
Keywords : global optimization, linearisations, constraint programming, interval analysis, numerical robustness, constraint satisfaction problems (CSP).
A safe and efficient framework for Solving Optimization
The use of interval methods provides computational proofs of existence and location of global optima. These methods find the global optimum and provide bounds on its value and location.
Efficient global optimization software like BARON use linear relaxations to compute a lower bound of the objective function, and local search methods to obtain an upper bound of the optima. However, these software are not safe and may provide wrong solutions.
We have introduced an efficient and safe framework to find a global optimum and bounds on its value . Local search methods are combined with interval techniques to compute a safe upper bound. Consistency techniques are also used to speed up the initial convergence of the interval narrowing algorithms. A lower bound is computed on a linear relaxation of the constraint system and the objective function. This computation is based on a safe and rigorous implementation of linear programming techniques.