Derivative-free Augmented Lagrangian Method For Nonlinear Optimization Problem

In this paper, we focus on the model-based derivative-free method. This method achieve the globally minimization point through minimize the objective function locally. Every iterate do not rely on derivative information of the objective function or constraints, nor designed explicitly to approximate these derivatives.This work is divided into two parts:In the first part, we consider the nonlinear equality constrained optimization problem. We proposed model-based derivative-free aug-mented lagrangian method, and give the global convergence of the new method. In the second part, we turn the model-based derivative-free augmented lagrangian method which made the appropriate adjustments, under certain conditions to solve the nonlinear con-strained optimization problem. Achieved the following results:1. Chapter 2 solve nonlinear equality constrained optimization problem. Com-bined the increase the A—balance check model-based method and augmented Lagrangian method, and used trust region framework, We proposed model-based augmented la-grangian method and the corresponding algorithm. This algorithm could have the first-order stationary point through less iterates. At last, we prove globally convergence of this algorithm.2. Chapter 3 solve nonlinear constrained optimization problem. Firstly we convert the original problem to equality constrained problem which is equip the relaxation vari-ables, and then use the modified algorithm of chapter 2 to solve it. At last, we prove the globally convergence of the modified algorithm of chapter 2 which point out that the limit points of optimal points of the original problem are first order stationary points.