A dual differentiable exact penalty function

1983 ◽  
Vol 25 (3) ◽  
pp. 293-306 ◽  
Author(s):  
S. -P. Han ◽  
O. L. Mangasarian
Keyword(s):  
Penalty Function ◽  
Exact Penalty Function ◽  
Exact Penalty

Smoothing Partially Exact Penalty Function of Biconvex Programming

2020 ◽  
Vol 37 (04) ◽  
pp. 2040018
Author(s):  
Rui Shen ◽  
Zhiqing Meng ◽  
Min Jiang
Keyword(s):  
Error Bounds ◽  
Penalty Function ◽  
Constraint Qualification ◽  
Feasible Solution ◽  
Exact Penalty Function ◽  
Exact Penalty ◽  
Kkt Condition ◽  
Optimum Point ◽  
Kkt Point ◽  
Slater Constraint Qualification

In this paper, a smoothing partial exact penalty function of biconvex programming is studied. First, concepts of partial KKT point, partial optimum point, partial KKT condition, partial Slater constraint qualification and partial exactness are defined for biconvex programming. It is proved that the partial KKT point is equal to the partial optimum point under the condition of partial Slater constraint qualification and the penalty function of biconvex programming is partially exact if partial KKT condition holds. We prove the error bounds properties between smoothing penalty function and penalty function of biconvex programming when the partial KKT condition holds, as well as the error bounds between objective value of a partial optimum point of smoothing penalty function problem and its [Formula: see text]-feasible solution. So, a partial optimum point of the smoothing penalty function optimization problem is an approximately partial optimum point of biconvex programming. Second, based on the smoothing penalty function, two algorithms are presented for finding a partial optimum or approximate [Formula: see text]-feasible solution to an inequality constrained biconvex optimization and their convergence is proved under some conditions. Finally, numerical experiments show that a satisfactory approximate solution can be obtained by the proposed algorithm.

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

1992 ◽  
Vol 55 (1-3) ◽  
pp. 49-68 ◽  
Author(s):  
Gianni Di Pillo ◽  
Francisco Facchinei ◽  
Luigi Grippo
Keyword(s):  
Penalty Function ◽  
Exact Penalty Function ◽  
Exact Penalty ◽  
Constrained Problems

A New Exact Penalty Function

2003 ◽  
Vol 13 (4) ◽  
pp. 1141-1158 ◽  
Author(s):  
Waltraud Huyer ◽  
Arnold Neumaier
Keyword(s):  
Penalty Function ◽  
Exact Penalty Function ◽  
Exact Penalty
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