Non-monotone Wedge Trust Region Methods For The Derivative-free Optimization

In this work,we research the non-monotone wedge trust region method.Wedge trust region algorithm is a kind of very effective method for solving derivative-free optimization.Actually,it is a trust region method subject to a special wedge constraint and this constraint is constructed for meeting with the so-called “poised” quality of the interpolation modal.On the other hand,the non-monotone technique can effectively deal with the martos effect of the constraint optimization problem.Especially,it is a very well method when the objective-function with a characteristics of steep and narrow valley.For the purpose of improving the operating efficiency of the wedge trust region algorithm,we introduce four non-monotone techniques to develop some hybridization algorithms which combine the wedge constraint with the non-monotone strategies.Furthermore,we have carried out a large number of numerical experiments for comparing the four non-monotone techniques with the original method.The numerical results show that the proposed non-monotone wedge trust region algorithm has a higher computational efficiency generally.Finally,we develop a new method called self-correcting geometry,which is a geometric correction step for getting a new better interpolation set.In this wok,we combine this method with the non-monotone wedge trust region algorithm,and this new method can guarantee the balance of interpolation point and accelerate its convergence.