Previous |  Up |  Next


equilibrium problems with complementarity constraints; homotopy; C-stationarity
In the paper we consider EPCCs with convex quadratic objective functions and one set of complementarity constraints. For this class of problems we propose a possible generalization of the homotopy method for finding stationary points of MPCCs. We analyze the difficulties which arise from this generalization. Numerical results illustrate the performance for randomly generated test problems.
[1] Jongen, H. T., Jonker, P., Twilt, F.: Nonlinear Optimization in Finite Dimensions. Kluwer, Dordrecht 2000. MR 1794354 | Zbl 0985.90083
[2] Leyffer, S., Munson, T.: A globally convergent filter method for MPECs. Preprint ANL/MCS-P1457-0907 (2007).
[3] Luo, Z.-Q., Pang, J.-S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge 1996. MR 1419501 | Zbl 0870.90092
[4] Murty, K. G.: Linear Complementarity, Linear and Nonlinear Programming. Helderman-Verlag 1988. MR 0949214 | Zbl 0634.90037
[5] Ralph, D., Stein, O.: The C-index: a new stability concept for quadratic programs with complementarity constraints, preprint 2010 (a revised version of Homotopy methods for quadratic programs with complementarity constraints. Preprint No. 120, Department of Mathematics - C, RWTH Aachen University 2006). MR 2832404
[6] Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity. Math. Oper. Res. 25 (2000), 1–22. DOI 10.1287/moor. | MR 1854317
[7] Scholtes, S., Stöhr, M.: How stringent is the linear independence assumption for mathematical programs with complementarity constraints? Math. Oper. Res. 26 (2001), 851–863. DOI 10.1287/moor.26.4.851.10007 | MR 1870748
[8] Su, C.-L.: Equilibrium Problems with Equilibrium Constraints: Stationarities, Algorithms and Applications. PhD Thesis, Department of Management Science and Engineering, Stanford University 2005.
Partner of
EuDML logo