# Numerical Methods for Disjunctive Programming

## Mag. Matúš Benko

**May 6, 2014, 1:30 p.m. S2 059**

In this talk, we consider mathematical programs with equilibrium constraints (MPEC for short) which have their origin in bilevel programming and arise in many applications in economic, engineering and natural sciences. MPECs are known to be difficult optimization problem because due to the complementarity conditions many of the standard constraints qualifications of nonlinear programming are violated at any feasible point. Hence various first-order optimality conditions have been studied (A-, B-, C-, M- and S-stationarity conditions).

While many other algorithms are only able to secure (weaker) C-stationarity, we present the algorithm that guarantees (stronger) M-stationarity of a limit point. The core of the algorithm lies in a sub-problem of solving quadratic problem (quadratic objective function with linear constrain functions). Moreover, this algorithm can be modified to obtain even stronger stationarity.