An Approach to Nonlinear Programming

作     者：Luenberger, D. G. 

作者机构：Stanford Univ Dept Engn Econ Syst Stanford CA 94305 USA 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：1973年第11卷第3期

页      面：219-227页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation [GK-16125] 

主　　题：Lagrange Multiplier Programming Problem Minimization Problem Global Minimum Original Problem 

摘      要：A nonlinear programming problem with inequality constraints and with unknown vector x is converted to an unconstrained minimization problem in unknowns x and lambda, where lambda is a vector of Lagrange multipliers. It is shown that, if the original problem possesses standard convexity properties, then local minima of the associated unconstrained problem are in fact global minima of that problem and, consequently, Kuhn-Tucker points for the original problem. A computational procedure based on the conjugate residual scheme is applied in the x lambda-space to solve the associated unconstrained problem. The resulting algorithm requires only first-order derivative information on the functions involved and will solve a quadratic programming problem in a finite number of steps.