A Filter Pattern Search Method For Linear Equality Constrained Optimization Problems

Recently, optimization methods have many applications in physics, chemistry, finance and many other fields. However, since the objective functions of some prac-tical applications are usually given by computer simulation, whose information of derivatives is unavailable, unreliable, or time-consuming. Therefore, we are urgent to develop some effective methods for solving these problems. Pattern search al-gorithm is an effective derivative-free methods. In this paper, we mainly discuss a pattern search method for linear equality constrained optimization problems.In Chapter2, we give some preliminaries, including pattern search algorithm, the difference and relations among generalized pattern search method, grid-based search method and frame-based search method, feasible direction method, and filter technique.In Chapter3, we focus on the transformation of the problem and the improve-ment of the pattern search algorithm framework and give a pattern search filter method for linear equality constrained optimization problems. Using feasible direc-tion method, we transform the linear equality constrained optimization problems to unconstrained ones. Then, by introducing filter technique as an improvement strat-egy, we apply it to pattern search method and solve the transformed optimization problems. Finally, convergence theory on the improved algorithm is given, and the numerical results to illustrate the effective of the improved algorithm are reported.