A class of smoothing methods for mathematical programs with complementarity constraints

2007 ◽  
Vol 186 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Tao Yan
Keyword(s):  
Complementarity Constraints ◽  
Smoothing Methods ◽  
Mathematical Programs

scholarly journals A New Smoothing Method for Mathematical Programs with Complementarity Constraints Based on Logarithm-Exponential Function

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Chen ◽  
Zhong Wan
Keyword(s):  
Approximate Solution ◽  
Exponential Function ◽  
Constraint Qualification ◽  
Mathematical Program ◽  
Accumulation Point ◽  
Smoothing Method ◽  
Complementarity Constraints ◽  
Smoothing Methods ◽  
Mathematical Programs ◽  
Solution Sequence

We present a new smoothing method based on a logarithm-exponential function for mathematical program with complementarity constraints (MPCC). Different from the existing smoothing methods available in the literature, we construct an approximate smooth problem of MPCC by partly smoothing the complementarity constraints. With this new method, it is proved that the Mangasarian-Fromovitz constraint qualification holds for the approximate smooth problem. Convergence of the approximate solution sequence, generated by solving a series of smooth perturbed subproblems, is investigated. Under the weaker constraint qualification MPCC-Cone-Continuity Property, it is proved that any accumulation point of the approximate solution sequence is a M-stationary point of the original MPCC. Preliminary numerical results indicate that the developed algorithm based on the partly smoothing method is efficient, particularly in comparison with the other similar ones.

A New Regularization Scheme for Mathematical Programs with Complementarity Constraints

2009 ◽  
Vol 20 (1) ◽  
pp. 78-103 ◽  
Author(s):  
Abdeslam Kadrani ◽  
Jean-Pierre Dussault ◽  
Abdelhamid Benchakroun
Keyword(s):  
Complementarity Constraints ◽  
Regularization Scheme ◽  
Mathematical Programs
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