# An SQP method for Mathematical Programs with Vanishing Constraints

## Mag. Matúš Benko

Nov. 3, 2015, 3:30 p.m. S2 059

In this talk we present an SQP method for Mathematical Programs with Vanishing Constraints (MPVC) which solves at each iteration a quadratic program with linear vanishing constraints (auxiliary problem). This method is based on well-known SQP method for nonlinear programming. However, due to the special type of constraints of MPVC, the feasible region of auxiliary problem is non-convex what makes the situation much more complicated and hence a suitable modification of SQP is required.
We demonstrate how $\beta$-stationary solutions of auxiliary problem can be obtained by solving convex pieces. We show the main result that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary. Finally, we introduce a modification of this SQP method and conclude that for this modified method, apart from M-stationarity of all limit points, we also obtain the existence of at least one $\beta$-stationary limit point.