| 求解约束规划的一个非线性Lagrange函数 |
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| 引用本文： | 顾剑,任咏红. 求解约束规划的一个非线性Lagrange函数[J]. 数学进展, 2007, 36(6): 749-760 |
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| 作者姓名： | 顾剑 任咏红 |
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| 作者单位： | 大连理工大学应用数学系,大连,辽宁,116024 |
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| 摘 要： | 本文提出了一个求解不等式约束优化问题的非线性Lagrange函数,并构造了基于该函数的对偶算法.证明了当参数σ小于某一阈值σ_0时,由算法生成的原始-对偶点列是局部收敛的,并给出了原始-对偶解的误差估计.此外,建立了基于该函数的对偶理论.最后给出了算法的数值结果.
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| 关 键 词： | 非线性Lagrange函数 对偶算法 对偶函数 鞍点 |
| 文章编号： | 1000-0917（2007）06-0749-12 |
| 收稿时间： | 2005-05-17 |
| 修稿时间： | 2006-06-30 |
A Nonlinear Lagrangian for Constrained Programming |
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| GU Jian,REN Yong-hong. A Nonlinear Lagrangian for Constrained Programming[J]. Advances in Mathematics(China), 2007, 36(6): 749-760 |
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| Authors: | GU Jian REN Yong-hong |
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| Abstract: | This paper establishes a nonlinear Lagrangian for solving nonlinear program- ming problems with inequality constraints.We prove that there exists a threshold such that the sequence of primal-dual iterate points generated by dual algorithm basing on the nonlinear Lagrangian locally converges to a minimizer if the penalty parameter is lower than the thresh- old.We also give the error bound of pimal-dual solutions.Moreover,we develop corresponding duality theory.Finally we report some numerical results by using the proposed dual algorithm. |
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| Keywords: | nonlinear Lagrangian dual algorithm dual function saddle point |
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