Trajectory Methods In Global Optimization

. We review the application of trajectory methods (not including homotopy methods) to global optimization problems. The main ideas and the most successful methods are described and directions of current and future research are indicated. Key words: Global Optimization, Continuous Newton Method, Trajectory Method. 1. Introduction Consider the following problem: Given a set B ae IR n and a continuous function F : B ! IR, determine f = inf x2B f(x) and some or all points in f \Gamma1 (f ) provided this set is nonempty. This is about the most general form a global optimization problem on a finite dimensional space can take. It includes discrete (combinatorial) optimization problems as well as continuous constraint and unconstraint problems. A related problem is: Given B ae IR n and a continuous map F : B ! IR n , determine some or all points in Zero(F; B) := F \Gamma1 (0). This includes fixed point problems and the solution of nonlinear equations. The above problems are obvi..