A New Type of Optimization Method Based on Conjugate Directions

A new type of optimization method based on conjugate directions is proposed in this paper. It can be proved that this type of method has quadratic termination property without exact line search. The new method requires only the storage of 4 vectors such that it is suitable for large scale problems. Numerical experiences show that the new method is effective.

A New Conjugate Direction Algorithm for Unconstrained Function Minimization

Based on the properties of conjugate vectors, a new algorithm for unconstrained function minimization is developed. The algorithm belongs to the direct search method and is a conjugate direction-type method with the property of quadratic termination. Comparing with some convensional direct search methods including the modified Powell method, the number of one dimensional search is greatly reduced. In addition, the algorithm presented in this paper is simple in calculating and easy in coding, and it has the capability of accelerating along the ridges. The method presented is compared with two direct search methods including the modified Powell method on many test problems. Numerical results show the robustness and efficiency of the new algorithm.