| 不等式约束优化问题的一个精确增广拉格朗日函数 |
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| 引用本文： | 杜学武,靳祯.不等式约束优化问题的一个精确增广拉格朗日函数[J].上海交通大学学报,2006,40(9):1636-1640. |
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| 作者姓名： | 杜学武 靳祯 |
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| 作者单位： | 1. 大连理工大学,应用数学系,大连,116024;河南理工大学,应用数学系,焦作,454010
2. 上海交通大学,数学系,上海,200240 |
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| 基金项目： | 河南省高校青年骨干教师资助项目;陕西省教育厅自然科学基金 |
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| 摘 要： | 给出了求解只带有不等式约束非线性规划问题的一个连续可微精确增广拉格朗日函数法,并讨论了它的精确性质.该方法的主要特点是:在适当的假设下,通过对这个增广拉格朗日函数在原问题变量和乘子变量的积空间上进行一个单一的无约束极小化,即可获得原约束问题的解,从而可以有效地使用标准的无约束极小化方法求解不等式约束非线性规划问题.
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| 关 键 词： | 最优化 非线性规划 约束最优化 增广拉格朗日函数 |
| 文章编号： | 1006-2467(2006)09-1636-05 |
| 收稿时间： | 2005-04-30 |
| 修稿时间： | 2005年4月30日 |
An Exact Augmented Lagrangian Function for Nonlinear Programming Problems with Inequality Constraints |
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| DU Xue-wu,JIN Zhen.An Exact Augmented Lagrangian Function for Nonlinear Programming Problems with Inequality Constraints[J].Journal of Shanghai Jiaotong University,2006,40(9):1636-1640. |
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| Authors: | DU Xue-wu JIN Zhen |
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| Institution: | 1. Dept. of Applied Mathematics, Dalian Univ. of Technology, Dalian 116024, China; 2. Dept. of Applied Mathematics, Henan Polytechnic Univ. , Jiaozuo 454010, China; 3. Dept. of Mathematics, Shanghai Jiaotong Univ. , Shanghai 200240, China |
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| Abstract: | A continuously differentiable exact augmented Lagrangian function was introduced for solving nonlinear nonconvex programming problems with inequality constraints and its exactness property was discussed.The relevant feature of the proposed approach is that,under suitable assumptions,it enables one to obtain the solution of the original constrained problem by a single unconstrained minimization of this augmented Lagrangian function on the product space of problem variables and multipliers,so that standard unconstrained minimization techniques can be employed for solving nonlinear programming problems with inequality constraints. |
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| Keywords: | optimization nonlinear programming constrained optimization augmented Lagrangian functions |
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