An Improvement Of Wedge Trust Region Algorithm

Wedge trust region method belongs to the derivative-free method, which uses theinformation of function values alone to find the optimum solution. As for the interpolationmodel in this method, the choice of the interpolation point is very important, namely, theirpositions need to meet the so-called “poised”.The present wedge trust region algorithm usually uses a single model for solution, butignores the relation between the locality and the entirety of the algorithm. As we all know,only when the iteration point is relatively close to the optimal point, does the quadratic modelhave higher degree of approximation with the function. Therefore, we consider using a hybridsearch algorithm combining linear model and quadratic model.The main task of this paper is as follows: first of all, we improve the constructionmethod of interpolating point set, the key point of which is to use the interpolation point set ofthe linear model to form the interpolation point set of the quadratic model. It can effectivelyavoid waste and take advantage of local information of the current iteration point in thealgorithm. Secondly, we improve the hybrid search algorithm using linear model andquadratic model by the above-mentioned construction method of the interpolation point set.When the iteration point is far away from the optimal point, the linear model is used. Whenthe iteration point is closer to the optimal point, the current linear model is used to construct aquadratic model. A lot of numerical experiments show that the algorithm improved by us hasa big advantage in terms of reducing the calculation times of function value.