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| EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS | |
| 引用本文： | 杜学武 张连生 尚有林 李铭明. EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS[J]. 应用数学和力学(英文版), 2005, 26(12): 1649-1656. DOI: 10.1007/BF03246275 |
| 作者姓名： | 杜学武 张连生 尚有林 李铭明 |
| 作者单位： | [1]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China [2]School of Mathematics and Informatics,Henan Polytechnic University, Jiaozuo 454010, Henan Province, P. R. China |
| 摘 要： | An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented. |
| 关 键 词： | 拉格朗日函数 非线性规划问题 补偿函数 局部最小化 |
| 文章编号： | 0253-4827（2005）12-1649-08 |
| 收稿时间： | 2004-02-01 |
| 修稿时间： | 2005-05-31 |
Exact augmented lagrangian function for nonlinear programming problems with inequality constraints |
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| Xue-wu Du,Lian-sheng Zhang,You-lin Shang,Ming-ming Li. Exact augmented lagrangian function for nonlinear programming problems with inequality constraints[J]. Applied Mathematics and Mechanics(English Edition), 2005, 26(12): 1649-1656. DOI: 10.1007/BF03246275 | |
| Authors: | Xue-wu Du Lian-sheng Zhang You-lin Shang Ming-ming Li |
| Affiliation: | 1. Department of Mathematics, Shanghai University,Shanghai 200444, P. R. China;School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan Province, P.R.China 2. Department of Mathematics, Shanghai University,Shanghai 200444, P. R. China |
| Abstract: | An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f~om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented. |
| Keywords: | local minimizer global minimizer nonlinear programming exact penalty function augmented Lagrangian function |
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