Some Researching On Derivative-free Optimization Block Decomposition

In the engineering application and multidisciplinary optimization, we often meet that the variables can be divided into two parts, one of which may be mediated, and the other can not, in this case, it will be used block decomposition method to solve. But we must introduce parameter when it has the constraint condition. In this context,the paper solve it by introducing the Lagrange block decomposition method, and get good results. But on the block decomposition method itself, the results we obtained are mainly directed against the unconstrained, and components are usually limited to two.This paper tentatively applied in solving constrained optimization problems, and obtained certain achievement.This thesis is organized as follows:The second chapter In this chapter, considering the nonlinear equality constraints, we introduce the Lagrange model from the literature eleven which changes the constrained optimization problem into unconstrained optimization problems, then combined with the block decomposition method for solving the problem.In proof of the stable point, this pa-per assumes that parameters and variables were unrelated, and we prove the convergence of the sequence’s convergence through the parameter convergence or show the parameters corresponding to the convergence of the sequence of points are stable set.The third chapter In this chapter,we study the optimization problem with equality and inequality constraints so that the optimization model is more common. By intro-ducing the extended Lagrange model from the literature thirty-one, we change it into the unconstrained conditions, then Combined with the block decomposition method for solving. In the proof of convergence we use the method from the literature thirty-one.