Paper Info
Title
Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints
Abstract
We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation is semismooth and BD-regular at the solution under reasonable assumptions. Thus, fast local convergence can be obtained by applying the semismooth Newton method. Moreover, it turns out that the squared residual of the Lagrange system is continuously differentiable (even though the system itself is not), which opens the way for a natural globalization of the local algorithm. Preliminary numerical results are also reported.
Year
DOI
Venue
2012
10.1007/s10589-010-9341-7
Computational Optimization and Applications
Keywords
Field
DocType
Mathematical program with complementarity constraints,Semismooth Newton method,BD,-regularity,Second-order sufficiency,Merit function
Complementarity (molecular biology),Residual,Mathematical optimization,Square (algebra),Differentiable function,Local convergence,Local algorithm,Smoothness,Mathematics,Newton's method
Journal
Volume
Issue
ISSN
46
2
0926-6003
Citations 
PageRank 
References 
11
0.65
16
Authors
3
Name
Order
Citations
PageRank
A. F. Izmailov123821.76
A. L. Pogosyan2131.37
M. V. Solodov360072.47