Pattern Search Methods For The Derivative-free Optimization

Pattern search algorithms is one of most often used methods which were designed to solve the derivative-free optimizaiton problems. In order to make the pattern search algorithm to obtain the numerical results better, this paper introduced a parameter m in the algorithm which controls the extension search after the successful iteration and makes full use of the current iteration of the decline for the information. We mean along the descent direction, we allow the algorithm go ahead m steps at most to explore whether we can get better solution.In addition, we also study on the the constrained optimization problems. During the running of the algorithm, it used the technique of a subspace, put forward a kind of derivative free optimization algorithm. Specifically when the algorithm found two different descent direction in the current iteration point, it incorporates the progressive obtained local information into the current iteration, then we can search at the composite direction. By doing these, a new point is produced through some kind of line search techniques.At last, we test the efficiency of our new method on the benchmarking. The computational results show the efficiency of the modified algorithm.