An Improvement Of Wedge Trust Region Algorithm For Nonlinear Optimization

Wedge trust region method based on traditional trust region is designed for derivativefree optimization problems. The novelty of wedge trust region is to add a constraint to thetrust region subproblem, which is called “wedge trust region”. In addition, the radius updaterules have a strong influence on the performance of an algorithm. In this paper, faced with thedisadvantages of the original radius update rule, we improve the algorithm from the angle ofquadratic and linear models respectively. When choosing the quadratic models, we propose amethod for updating radius; at the same time, we also proposed two methods for linearmodels to update the radius. For most test problems, the experiments demonstrate thenumbers of function evaluations of the three methods are both reduced significantlycompared with the former one.Finally, we consider combining the two versions of models to solve the derivative freeoptimization problems. We would choose linear models in the initial stages of our algorithm.If some certain conditions are satisfied we will use quadratic models; otherwise, continue touse the linear models until the algorithm terminates. Then, we compared the improved wedgetrust region algorithm with the algorithm containing just one version of models. Theexperimental results demonstrate that the method of hybrid model in the wedge trust regionframework is better than using only one version of models in this algorithm, and the newalgorithm is more effective on the majority of test problems.