Conic Optimization, Cone-Complementarity Problems and applications
There is a nice theory for Cone-complementarity problems defined by general cones. See for example "Finite-Dimensional Variational Inequalities and Complementarity Problems: Springer Series in Operations Research, by Francisco Facchinei and Jong-Shi Pang 2003 or 2013" and "Equilibrium Models and Variational Inequalities (Mathematics in Science & Engineering) by Igor Konnov, Butterworth-Heinemann 2007". However, when it comes to practical problems most of them are related to the nonnegative orthant. By using the KKT conditions a correspondence between the cone-complementarity problems and conic optimization problems can be made. Therefore, several problems from economics, engineering and physics which can be modelled by conic optimization can be also modelled by cone-complementarity problems. Usually the cone is the second order cone, the positive semidefinite cone or direct products of such cones. The project will investigate cone-complementarity problems and their applications. However, the project will also investigate the possibility for so called "essential applications" of cone-complementarity problems, when the complementarity problem does not come from a conic optimization problem and the cone is essentially different from the nonnegative orthant.
This is a very demanding project and I accept only very good and committed students. A comfortable first class (or equivalent) is a must.
Francisco Facchinei and Jong-Shi Pang: Finite-Dimensional Variational Inequalities and Complementarity Problems: Springer Series in Operations Research, 2003 or 2013
Igor Konnov: Equilibrium Models and Variational Inequalities (Mathematics in Science & Engineering) Butterworth-Heinemann 2007
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