Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/26090
Title: Nonlinear Lagrangian theory for nonconvex optimization
Authors: Goh, CJ
Yang, XQ 
Keywords: Inequality constraints
Nonconvex optimization
Nonlinear Lagrangian
Sufficient and necessary conditions
Zero duality gap
Issue Date: 2001
Publisher: Springer
Source: Journal of optimization theory and applications, 2001, v. 109, no. 1, p. 99-121 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: The Lagrangian function in the conventional theory for solving constrained optimization problems is a linear combination of the cost and constraint functions. Typically, the optimality conditions based on linear Lagrangian theory are either necessary or sufficient, but not both unless the underlying cost and constraint functions are also convex. We propose a somewhat different approach for solving a nonconvex inequality constrained optimization problem based on a nonlinear Lagrangian function. This leads to optimality conditions which are both sufficient and necessary, without any convexity assumption. Subsequently, under appropriate assumptions, the optimality conditions derived from the new nonlinear Lagrangian approach are used to obtain an equivalent root-finding problem. By appropriately defining a dual optimization problem and an alternative dual problem, we show that zero duality gap will hold always regardless of convexity, contrary to the case of linear Lagrangian duality.
URI: http://hdl.handle.net/10397/26090
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1023/A:1017513905271
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

19
Last Week
0
Last month
0
Citations as of Oct 10, 2017

WEB OF SCIENCETM
Citations

16
Last Week
0
Last month
0
Citations as of Oct 24, 2017

Page view(s)

28
Last Week
1
Last month
Checked on Oct 22, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.