Continuous Global Optimization based on Contractor Programming
Résumé
Contractor Programming is a methodology which allows to enclose each algorithm in a unify framework, in order to interact heterogeneous formulations or techniques. In this talk, we will present a general pattern based on contractor programming for designing a global optimization solver. This approach is based on Interval Analysis and can deal with problems with a wide variety of constraints. Using Contractor Programming, we will show a user-friendly way to solve problems with non-smooth functions, disjunctive constraints, non-mathematical constraints (such as "stay in an area defined by a polygon") and constraints with quantifiers (such as ForAll and Exists).
This approach allows to design, in a single step, a model and a solver for a given problem. This framework is implemented in the library IBEX (http ://www.ibex-lib.org) which is free available. The goal of this library is to give all tools to the users for designing easily the best solver for its own problem.