Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simulated annealing, on four econometric problems and compare it to three common conventional algorithms. Not only can simulated annealing find the global optimum, it is also less likely to fail on difficult functions because it is a very robust algorithm. The promise of simulated annealing is demonstrated on the four econometric problems.

. 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...

this paper both involve the determination of the structure of clusters of atoms or molecules, but each application uses a di#erent potential energy function. The first potential is given by the sum of the pairwise interactions between atoms described by the Lennard-Jones function, and the second is the empirical water dimer potential energy surface function (RWK2-M) described in [10]. Problems in determining molecular structure lead to optimization problems because the naturally occurring structure usually minimizes the potential energy of the system. These problems become global optimization problems because typically such functions have very many local minimizers.

functions with simulated annealing*