@phdthesis{Schwartz2011,
  author    = {Schwartz, Alexandra},
  title     = {Mathematical Programs with Complementarity Constraints: Theory, Methods and Applications},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-64891},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2011},
  abstract  = {The subject of this thesis are mathematical programs with complementarity conditions (MPCC). At first, an economic example of this problem class is analyzed, the problem of effort maximization in asymmetric n-person contest games. While an analytical solution for this special problem could be derived, this is not possible in general for MPCCs. Therefore, optimality conditions which might be used for numerical approaches where considered next. More precisely, a Fritz-John result for MPCCs with stronger properties than those known so far was derived together with some new constraint qualifications and subsequently used to prove an exact penalty result. Finally, to solve MPCCs numerically, the so called relaxation approach was used. Besides improving the results for existing relaxation methods, a new relaxation with strong convergence properties was suggested and a numerical comparison of all methods based on the MacMPEC collection conducted.},
  subject      = {Zwei-Ebenen-Optimierung},
  language  = {en}
}
@phdthesis{Hoheisel2009,
  author    = {Hoheisel, Tim},
  title     = {Mathematical Programs with Vanishing Constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-40790},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {A new class of optimization problems name 'mathematical programs with vanishing constraints (MPVCs)' is considered. MPVCs are on the one hand very challenging from a theoretical viewpoint, since standard constraint qualifications such as LICQ, MFCQ, or ACQ are most often violated, and hence, the Karush-Kuhn-Tucker conditions do not provide necessary optimality conditions off-hand. Thus, new CQs and the corresponding optimality conditions are investigated. On the other hand, MPVCs have important applications, e.g., in the field of topology optimization. Therefore, numerical algorithms for the solution of MPVCs are designed, investigated and tested for certain problems from truss-topology-optimization.},
  subject      = {Nichtlineare Optimierung},
  language  = {en}
}
@phdthesis{Flegel2005,
  author    = {Flegel, Michael L.},
  title     = {Constraint qualifications and stationarity concepts for mathematical programs with equilibrium constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-12453},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {An exhaustive discussion of constraint qualifications (CQ) and stationarity concepts for mathematical programs with equilibrium constraints (MPEC) is presented. It is demonstrated that all but the weakest CQ, Guignard CQ, are too strong for a discussion of MPECs. Therefore, MPEC variants of all the standard CQs are introduced and investigated. A strongly stationary point (which is simply a KKT-point) is seen to be a necessary first order optimality condition only under the strongest CQs, MPEC-LICQ, MPEC-SMFCQ and Guignard CQ. Therefore a whole set of KKT-type conditions is investigated. A simple approach is given to acquire A-stationarity to be a necessary first order condition under MPEC-Guiganrd CQ. Finally, a whole chapter is devoted to investigating M-stationary, among the strongest stationarity concepts, second only to strong stationarity. It is shown to be a necessary first order condition under MPEC-Guignard CQ, the weakest known CQ for MPECs.},
  subject      = {Nichtlineare Optimierung},
  language  = {en}
}