Applications of Public Domain Global Optimization Software to Di cult Econometric Functions

Finding the global optimum can be challenging. The value located by a deterministic algorithm, such as Newton's method, will depend on the starting point used. Some starting points will lead to the global optimum while others will lead to a local optima. If there are a large number of local optima, nding the global optimum, in the absence of any other information, will largely be a matter of luck. Random search strategies are discussed in Sec. 2. A particular type of e cient random search, simulated annealing, is discussed in Sec. 3. A second type of e cient random search, genetic algorithms, is discussed in Sec. 4. Sec 5 considers evolutionary strategies, yet another search method and Sec 5.1 discusses a random search method combined with a deterministic search method. A list of the sources of the software used in this paper is given in Sec. 6. These algorithms are applied to di cult problems in Secs 789. Conclusions are presented in Sec. 10.