Existence of Local Saddle Points for a New Augmented Lagrangian Function

Wenling Zhao; Jing Zhang; Jinchuan Zhou

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Existence of Local Saddle Points for a New Augmented Lagrangian Function

机译：一个新的增广拉格朗日函数的局部鞍点的存在

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摘要

We give a new class of augmented Lagrangian functions for nonlinear programming problem with both equality and inequality constraints. The close relationship between local saddle points of this new augmented Lagrangian and local optimal solutions is discussed. In particular, we show that a local saddle point is a local optimal solution and the converse is also true under rather mild conditions.

机译：对于具有相等和不等式约束的非线性规划问题，我们给出了一类新的增广的拉格朗日函数。讨论了这种新的增强拉格朗日算子的局部鞍点与局部最优解之间的紧密关系。特别是，我们表明，局部鞍点是局部最优解，在相当温和的条件下，反之亦成立。

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来源
《Mathematical Problems in Engineering》 |2010年第3期|p.51-63|共13页
作者
Wenling Zhao; Jing Zhang; Jinchuan Zhou;
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Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China;

Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China;

Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China;

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1. Existence of Local Saddle Points for a New Augmented Lagrangian Function [J] . WenlingZhao, JingZhang, JinchuanZhou Mathematical Problems in Engineering: Theory, Methods and Applications . 2010,第2期

机译：一个新的增广拉格朗日函数的局部鞍点的存在
2. Augmented Lagrangian functions for cone constrained optimization: the existence of global saddle points and exact penalty property [J] . Dolgopolik M. V. Journal of Global Optimization . 2018,第2期

机译：锥约束优化的增强拉格朗日函数：全局鞍点的存在和精确的罚性质
3. Global saddle points of nonlinear augmented Lagrangian functions [J] . Wang Changyu, Liu Qian, Qu Biao Journal of Global Optimization . 2017,第1期

机译：非线性扩充拉格朗日函数的全局鞍点
4. Local Saddle Points Theory of a New Augmented Lagrangians [C] . Wenling Zhao, Jing Zhang, Jinchuan Zhou IITA International Conference on Nanotechnology and Computer Engineering . 2010

机译：新增强拉格朗人的本地马鞍要素理论
5. Existence and Regularity of Minimizers for Nonlocal Functionals [D] . Wright, Cory 2018

机译：非局部函数极小化的存在性和正则性
6. Saddle point localization of molecular wavefunctions [O] . Georg Ch. Mellau, Alexandra A. Kyuberis, Oleg L. Polyansky, -1

机译：分子波函数的鞍点定位
7. Augmented Lagrangian Functions for Cone Constrained Optimization: the Existence of Global Saddle Points and Exact Penalty Property [O] . Dolgopolik, M. V. 2017

机译：锥约束优化的增广拉格朗日函数：全球鞍点的存在与确切的刑罚性质
8. Existence of Saddle Points for Classes of Convex and Non-Convex Functions. [R] . aubin,jean pierre 1973

机译：凸和非凸函数类的鞍点存在性。

Existence of Local Saddle Points for a New Augmented Lagrangian Function

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