Parallel Continuous Non-Convex Optimization

Abstract

Parallel globed optimization is one very promising area of research since due to inherent difficulty of the problems it studies, only instances of limited dimension can be solved in reasonable computer time on conventional machines. However, the use of parallel and distributed processing can substantially increase the possibilities for the success of the global optimization approach in practice. In this chapter we are concerned with the development of parallel algorithms for solving certain classes of non-convex optimization problems. We present an introductory survey of exact parallel algorithms that have been used to solve structured (partially separable) problems and problems with simple constraints, and algorithms based on parallel local search and its deterministic or stochastic refinements for solving general non-convex problems. Indefinite quadratic programming, posynomial optimization, and the general global concave minimization problem can be solved using these approaches. In addition, the minimum concave cost network flow problem and location problems with economies of scale are used in illustrating these techniques for the solution of large-scale, structured problems.