一般非线性规划问题的凝聚同伦内点方法  

Aggregate Homotopy Interior-Point Method for General Nonlinear Programming Problems

作　　者：金鉴禄[1] 谭佳伟[1] 贺莉[1] 刘庆怀[1] 

机构地区：[1]长春工业大学基础科学学院,长春130012

出　　处：《吉林大学学报（理学版）》2011年第6期1044-1052,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10771020);吉林省自然科学基金(批准号:20101597)

摘　　要：考虑带有等式约束的一般非线性规划问题,先用极大值函数把不等式约束等价地表示为一个不光滑的不等式约束,并采用凝聚方法把不等式约束函数进行带参数的磨光,再利用组合同伦内点方法在广义弱法锥条件下,构造性地证明了广义K-K-T方程解的存在性和凝聚同伦方法的整体收敛性.数值结果表明该方法是有效的.We studied the problems of general nonlinear programming with equality constrains. First, the inequality constrain was expressed as an non-smooth inequality constrain by means of the max-value function, then with aggregate technique this constrain was smoothed. With the help of combined homotopy interior-point method and the weak normal condition, the existence of solution of the generalized K-K-T equation was verified. The algorithm was proved to be globally convergent. The results of numerical experiments show that the algorithm is effective and convenient.

关 键 词：非线性规划 凝聚函数 同伦方法 

分 类 号：O221.2[理学—运筹学与控制论]