Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems

Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multi...

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Main Authors: Yue Wang, Jinchuan Zhou, Jingyong Tang
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Mathematical and Computational Applications
Subjects:
generalized augmented Lagrange multipliers
saddle points
duality theory
Online Access:https://www.mdpi.com/2297-8747/25/2/24
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spelling doaj-749a1561f764402d94c4063fd4fcb69e2020-11-25T02:00:30ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-04-0125242410.3390/mca25020024Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization ProblemsYue Wang0Jinchuan Zhou1Jingyong Tang2Department of Statistics, School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, ChinaDepartment of Statistics, School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, ChinaSchool of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, ChinaThe augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed.https://www.mdpi.com/2297-8747/25/2/24generalized augmented Lagrange multiplierssaddle pointsduality theory
collection DOAJ
language English
format Article
sources DOAJ
author Yue Wang
Jinchuan Zhou
Jingyong Tang
spellingShingle Yue Wang
Jinchuan Zhou
Jingyong Tang
Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems
Mathematical and Computational Applications
generalized augmented Lagrange multipliers
saddle points
duality theory
author_facet Yue Wang
Jinchuan Zhou
Jingyong Tang
author_sort Yue Wang
title Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems
title_short Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems
title_full Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems
title_fullStr Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems
title_full_unstemmed Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems
title_sort existence of generalized augmented lagrange multipliers for constrained optimization problems
publisher MDPI AG
series Mathematical and Computational Applications
issn 1300-686X
2297-8747
publishDate 2020-04-01
description The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed.
topic generalized augmented Lagrange multipliers
saddle points
duality theory
url https://www.mdpi.com/2297-8747/25/2/24
work_keys_str_mv AT yuewang existenceofgeneralizedaugmentedlagrangemultipliersforconstrainedoptimizationproblems
AT jinchuanzhou existenceofgeneralizedaugmentedlagrangemultipliersforconstrainedoptimizationproblems
AT jingyongtang existenceofgeneralizedaugmentedlagrangemultipliersforconstrainedoptimizationproblems
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