A new exact exponential penalty function method and nonconvex mathematical programming

A new exact penalty function method, called the l 1 exact exponential penalty function method, is introduced. In this approach, the so-called the exponential penalized optimization problem with the l 1 exact exponential penalty function is associated with the original optimization problem with both...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 217; no. 15; pp. 6652 - 6662
Main Author: Antczak, Tadeusz
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.04.2011
Elsevier
Subjects:
Absolute value exponential penalty function
Calculus of variations and optimal control
Computation
Exact sciences and technology
Exponential penalized optimization problem
Inequalities
l1 exact exponential penalty function method
Lower bounds
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Optimization
Penalty function
r-Invex function with respect to η
Sciences and techniques of general use
Special functions
l 1 exact exponential penalty function method
Absolute value exponential penalty function
Exponential penalized optimization problem
r-Invex function with respect to η
Lower bound
exact exponential penalty function method
Optimization method
Mathematical method
l
Exponential function
Penalty method
Mathematical function
Exponential penalized optimization
Numerical analysis
problem
Applied mathematics
Optimal solution
Inequality constraint
Equality constraint
Variational calculus
Mathematical programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Description
Summary:A new exact penalty function method, called the l 1 exact exponential penalty function method, is introduced. In this approach, the so-called the exponential penalized optimization problem with the l 1 exact exponential penalty function is associated with the original optimization problem with both inequality and equality constraints. The l 1 exact exponential penalty function method is used to solve nonconvex mathematical programming problems with r-invex functions (with respect to the same function η). The equivalence between sets of optimal solutions of the original mathematical programming problem and of its associated exponential penalized optimization problem is established under suitable r-invexity assumption. Also lower bounds on the penalty parameter are given, for which above these values, this result is true.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.01.051