Numerical Methods for Disjunctive Programming

Mag. Matúš Benko

May 6, 2014, 3:30 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.