@phdthesis{vonHeusinger2009,
  author    = {von Heusinger, Anna},
  title     = {Numerical Methods for the Solution of the Generalized Nash Equilibrium Problem},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47662},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {In the generalized Nash equilibrium problem not only the cost function of a player depends on the rival players' decisions, but also his constraints. This thesis presents different iterative methods for the numerical computation of a generalized Nash equilibrium, some of them globally, others locally superlinearly convergent. These methods are based on either reformulations of the generalized Nash equilibrium problem as an optimization problem, or on a fixed point formulation. The key tool for these reformulations is the Nikaido-Isoda function. Numerical results for various problem from the literature are given.},
  subject      = {Spieltheorie},
  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{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{Teichert2009,
  author    = {Teichert, Christian},
  title     = {Globale Minimierung von Linearen Programmen mit Gleichgewichtsrestriktionen und globale Konvergenz eines Filter-SQPEC-Verfahrens f{\"u}r Mathematische Programme mit Gleichgewichtsrestriktionen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-38700},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {Mathematische Programme mit Gleichgewichtsrestriktionen (oder Komplementarit{\"a}tsbedingungen), kurz MPECs, sind als {\"a}ußerst schwere Optimierungsprobleme bekannt. Lokale Minima oder geeignete station{\"a}re Punkte zu finden, ist ein nichttriviales Problem. Diese Arbeit beschreibt, wie man dennoch die spezielle Struktur von MPECs ausnutzen kann und mittels eines Branch-and-Bound-Verfahrens ein globales Minimum von Linearen Programmen mit Gleichgewichtsrestriktionen, kurz LPECs, bekommt. Des Weiteren wird dieser Branch-and-Bound-Algorithmus innerhalb eines Filter-SQPEC-Verfahrens genutzt, um allgemeine MPECs zu l{\"o}sen. F{\"u}r das Filter-SQPEC Verfahren wird ein globaler Konvergenzsatz bewiesen. Außerdem werden f{\"u}r beide Verfahren numerische Resultate angegeben.},
  subject      = {Nichtlineare Optimierung},
  language  = {de}
}
@phdthesis{Lageman2007,
  author    = {Lageman, Christian},
  title     = {Convergence of gradient-like dynamical systems and optimization algorithms},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-23948},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {This work studies the convergence of trajectories of gradient-like systems. In the first part of this work continuous-time gradient-like systems are examined. Results on the convergence of integral curves of gradient systems to single points of Lojasiewicz and Kurdyka are extended to a class of gradient-like vector fields and gradient-like differential inclusions. In the second part of this work discrete-time gradient-like optimization methods on manifolds are studied. Methods for smooth and for nonsmooth optimization problems are considered. For these methods some convergence results are proven. Additionally the optimization methods for nonsmooth cost functions are applied to sphere packing problems on adjoint orbits.},
  subject      = {Dynamisches System},
  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}
}