## On Solving Mathematical Programs With Complementarity Constraints As Nonlinear Programs (2002)

Citations: | 33 - 2 self |

### BibTeX

@MISC{Anitescu02onsolving,

author = {Mihai Anitescu},

title = {On Solving Mathematical Programs With Complementarity Constraints As Nonlinear Programs},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

. We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using classical algorithms and procedures from nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier set to be nonempty in two different formulations. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can be approached by the elastic mode with a boundedpenalty parameter. This transformsthe MPCC into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem, which in turn makes it approachable by a sequential quadratic programming algorithm. The robustness of the elastic mode when applied to MPCCs is demonstrated by several numerical examples. 1. Introduction. Complementarity constraints can be used to model numerous economics or mechanics applications [18, 25]....