Trust Region Method Of New Conic Model For Nonlinearly Equality Constrained Optimization

Trust region methods possess robust and strong global convergence properties, conic model is generalization of quadratic model, and the combination of trust region techniques and conic model methods may form more powerful methods. The new trust region subproblem with conic model proposed in 2005 cancelled the restriction on the level vector, the subproblem was divided into three cases and trust region subproblems with new conic model were established. This paper applies new trust region subproblem with conic model to nonlinearly equality constrained optimization for the first time, a trust region algorithm based on new conic models for this problems is given, and its convergence is proved, numerical experiment is implemented.This paper includes four chapters. In Chapter 1, we introduce the research content and trust region method based on conic model briefly. Chapter 2 mainly focuses on subproblem. First, we convert the original problem to trust region subproblem subject to the linear constraints in the current iterate point, and remove the linear constraints using null-space technology. Then the subproblem is divided into three different cases, and the existing conic model algorithm is used to solve this subproblem. Base on these a trust region algorithm for solving subproblem is proposed. In Chapter 3, by selecting the appropriate merit function and using the frame of trust region, we give a description of the new conic trust region algorithm for nonlinearly constrained optimization, and prove its convergence under some conditions. In Chapter 4, we carry out numerical comparison experiments about the algorithm in Chapter 3, analyze numerical results, and draw useful conclusions. The theoretic and numerical results show that the algorithm in this paper is efficient and promising.