Research On Trust-region Algorithms For Derivative-free Optimization

There are many derivative-free optimization problems in the national defense construction and agriculture industry.Mesh adaptive direct search algorithm,simplex method and trust region method are effective methods to solve non-derivative optimization problems.Among them,the trust region method has a good experimental effect to deal with these optimization problem so that becomes one of the most active research fields.Conejo etc proposes an effective algorithm(TRDF).However,the TRDF algorithm ignores the relationship between the approximate update of the model and the initial Lagrange multiplier,lead to the increasing of the computational amount of the multiplier update.In order to solve the problem,two improved algorithms are proposed based on the existed algorithm to solve the non-derivative optimization problem.Based on the traditional trust region methods,we present an improved trust-region derivative-free algorithm.In the proposed method,we establish the constrain violation function and take advantage of the progressive barrier strategy-PB strategy to choose a better iteration point,and try to modify the initial augmented Lagrange multiplier.The improved trust-region derivative-free method can reduce the number of iteration and save the time in solving problems.Based on the TRDF algorithm framework,the generalized Lagrange function method is used to solve the trust region domain subproblem.We will establish the constraint violation function of the constraint conditions.At the same time,the PB strategy is used to search the experimental sites and find the points that meet certain constraints and reduce the value of the objective function.We propose a modified derivative-free trust region algorithm based on PB strategy,and the convergence of the algorithm is proved.The new algorithm effectively reduces the number of iterations and save the iterations time.