The l1 exact G-penalty function method and G-invex mathematical programming problems

In this paper, we consider G-invex mathematical programming problems and show the efficiency of G-invexity notion in proving optimality results for such nonconvex optimization problems. Further, we introduce a new exact penalty function method, called the l₁ exact G-penalty function method and use i...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 54; no. 9-10; pp. 1966 - 1978
Main Author: ANTCZAK, Tadeusz
Format: Journal Article
Language:English
Published: Kidlington Elsevier 01.11.2011
Subjects:
Calculus of variations and optimal control
computer techniques
decision making
Exact sciences and technology
Mathematical analysis
mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
system optimization
Lower bound
G-penalized optimization problem
Optimization method
Exact G-penalty function method
Mathematical method
Penalty method
Numerical analysis
Applied mathematics
Optimal solution
Absolute value G-penalty function
Mathematical model
G-invex function with respect to η
Computer aided analysis
Mathematical programming
ISSN:0895-7177
Online Access:Get full text
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Summary:In this paper, we consider G-invex mathematical programming problems and show the efficiency of G-invexity notion in proving optimality results for such nonconvex optimization problems. Further, we introduce a new exact penalty function method, called the l₁ exact G-penalty function method and use it to solve nonconvex mathematical programming problems with G-invex functions. In this method, the so-called exact G-penalized optimization problem associated with the original optimization problem is constructed. The equivalence between the sets of optimal solutions of the original mathematical programming problem and of its associated G-penalized optimization problem is established under suitable G-invexity assumptions. Also lower bounds on the penalty parameter are given, for which above this result is true. It turns out that, for some nonconvex optimization problems, it is not possible to prove the same result for the classical l₁ penalty function method under invexity assumption.
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ISSN:0895-7177
DOI:10.1016/j.mcm.2011.05.003