scholarly journals On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem

2012 ◽  
Vol 8 (2) ◽  
pp. 485-491 ◽  
Author(s):  
Changjun Yu ◽  
◽  
Kok Lay Teo ◽  
Liansheng Zhang ◽  
Yanqin Bai ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Convergence Analysis ◽  
Penalty Function ◽  
Function Method ◽  
Optimization Problem ◽  
Exact Penalty Function ◽  
Penalty Function Method ◽  
Exact Penalty ◽  
Constrained Optimization Problem ◽  
Inequality Constrained Optimization

THE l1 PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS

2010 ◽  
Vol 27 (05) ◽  
pp. 559-576 ◽  
Author(s):  
TADEUSZ ANTCZAK
Keyword(s):  
Penalty Function ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Exact Penalty Function ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Exact Penalty ◽  
Penalized Optimization

In this paper, some new results on the l1 exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l1 exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l1 exact penalty function is also established.

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