The New Butterfly Relaxation Method for Mathematical Programs with Complementarity Constraints

The New Butter y Relaxation Method for Mathematical Programs with Complementarity Constraints

We propose a new family of relaxation schemes for mathematical programs 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 our relaxation schemes has the de...

A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints

Regularization Method for Stochastic Mathematical Programs with Complementarity Constraints

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We ...

Levenberg-Marquardt Method for Mathematical Programs with Linearly Complementarity Constraints

In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.

Smoothing method for mathematical programs with symmetric cone complementarity constraints

In this paper, we consider the mathematical program with symmetric cone complementarity constraints (MPSCCC) in a general form. It includes the mathematical program with second-order-cone complementarity constraints (MPSOCCC) and the mathematical program with complementarity constraints (MPCC). We present a smoothing method which approximates the primal MPSCCC by means of the ChenMangasarian cl...