求解非线性约束优化问题的一类Lagrange算法.pdfVIP

(NLP) ℄ NLP KKT NLP KKT KKT KKT Æ 1.  ÆÆ KKT KKT Lagrange Lagrange 2. Æ  Æ Lagrange Lagrange KKT Abstract The constrained nonlinear programming problems (NLP) is a very important compo- nent part in operations research, It has wide application in natural science,engineering and economics. The typical method for solving NLP have feasible direction method, penalty function method, multiplier method , sequential quadratic programming and so on. In recent years, the method that a local minimum of NLP is obtained by solving KKT-systems for NLP becomes one of the efficient numerical methods for NLP. The main idea of the method is to reformulate the KKT-conditions for NLP as smooth nonlinear equations, then a KKT-point for NLP is obtained by using classical numerical methods for the problem . The methods in this thesis a KKT-point is obtained, but the difference train of thought to solve the problem. The specific contents are as follows: 1. The first we construct a new auxiliary function containing parameter, using the good propertys of this function.The constraint optimization problems with inequality constraints into equivalent conversion. This conversion not only ensure the KKT-condition of the new problems and the KKT-condition of the original problems with the solution, but also the introduction of parameters make the Lagrange function of the new problems with a penalty function . Using this characteristic, we propose a n