Existing methods for solving such problems can be shown to converge only under some restrictive assumption and it cannot precluded that they converge to points where spurious directions of descent exist.

Very recently the proposer has developed new stationarity concepts for the problem under consideration, which are based on generalized differentiation. The new algorithms shall rely on these new stationarity concepts and we want to prove global convergence properties under fairly mild assumptions. Further, superlinear convergence and the behaviour in the degenerate case are to be analyzed.

The new method has a similar structure as the well-known SQP method from nonlinear programming: In each iteration step an auxialiary problem is solved, where a quadratic objective function built by an approximation of the Hessian of the Lagrangefunction and the gradient of the objective, is minimized over the linearization of the constarint. Then a search is performed along the arc computed when solving this auxiliary problem in order to reduce a suitable merit function.

Helmut Gfrerer (Project leader)

Matuš Benko

- H.Gfrerer, Optimality conditions for disjunctive programs based on generalized differentiation with application to mathematical programs with equilibrium constraints, SIAM J. Optim., 24 (2014), pp. 898-931. Accepted Manuscript
- H. Gfrerer, J.V. Outrata, On computation of generalized derivatives of the normal-cone mapping and their applications, Math. Oper. Res. 41 (2016), pp. 1535-1556. Accepted Manuscript
- H. Gfrerer, J.V. Outrata, On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications, Optimization 65 (2016), pp. 671-700. Accepted Manuscript
- H. Gfrerer, B.S. Mordukhovich, Complete characterizations of tilt stability in nonlinear programming under weakest qualification conditions, SIAM J. Optim., 25 (2015), pp. 2081-2119. Accepted Manuscript
- H. Gfrerer, J.V. Outrata, On Lipschitzian properties of implicit multifunctions, SIAM J. Optim., 26 (2016), pp. 2160-2189. Accepted Manuscript
- H. Gfrerer, D.Klatte, Lipschitz and Hölder stability of optimization problems and generalized equations, Math. Program., 158 (2016), pp.35-75. Accepted Manuscript
- M. Benko, H. Gfrerer, An SQP method for mathematical programs with complementarity constraints with strong convergence properties, Kybernetika, 52 (2016), pp. 169-208.
- M. Benko, H. Gfrerer, On estimating the regular normal cone to constraint systems and stationarity conditions, Optimization 66 (2017), pp. 61-92. Accepted Manuscript
- M. Benko, H. Gfrerer, An SQP method for mathematical programs with vanishing constraints with strong convergence properties, 2016, to appear in Comput. Optim. Appl., Accepted Manuscript
- H. Gfrerer, B.S. Mordukhovich, Robinson stability of parametric constraint systems via variational analysis, 2016, to appear in SIAM J. Optim., Accepted Manuscript
- H.Gfrerer, J.J. Ye, New constraint qualifications for
mathematical programs with equilibrium constraints via
variational analysis, 2016, to appear in SIAM J. Optim., Accepted Manuscript

- M. Benko, H. Gfrerer, New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints, 2016, submitted. Preprint
- M.Benko, Numerical methods for mathematical programs with
disjunctive constraints, PhD-Thesis,
Univ.Linz, 2016