Vertex ordering with optimal number of adjacent predecessors

In this paper, we study the complexity of the selection of a graph discretization order with a stepwise linear cost function.Finding such vertex ordering has been proved to be an essential step to solve discretizable distance geometry problems (DDGPs). DDGPs constitute a class of graph realization problems where the vertices can be ordered in such … Read more

The New Butterfly Relaxation Methods for Mathematical Program with Complementarity Constraints

We propose a new family of relaxation schemes for mathematical program with complementarity constraints that extends the relaxations of Kadrani, Dussault, Bechakroun from 2009 and the one of Kanzow \& Schwartz from 2011. We discuss the properties of the sequence of relaxed non-linear program as well as stationarity properties of limiting points. A sub-family of … Read more

How to Compute a M-stationary point of the MPCC

We discuss here the convergence of relaxation methods for MPCC with approximate sequence of stationary points by presenting a general framework to study these methods. It has been pointed out in the literature, \cite{kanzow2015}, that relaxation methods with approximate stationary points fail to give guarantee of convergence. We show that by defining a new strong … Read more