PGMO Course 2014
May 5th, 2014, Ensta - "Bi-level stochastic programming"
Georg Pflug (University of Vienna)
Quite often, the result of our decisions depend on the action of others. A typical example is the setting of contracts, where the price is set by one party and the way how the contract is executed is decided by another party. These are examples of hierarchical leader-follower games of the Stackelberg type. We introduce stochastic Stackelberg games and demonstrate their complexity. Necessary optmality conditions are presented. A particular difficulty is due to the fact that even in linear situations the upper level feasible set may be non convex and disconnected. In particular, flexible electricity delivery contracts, called swing options are considered. In this case we are able to use a specially taylored a solution algorithm. since the upper level problem is univariate. We give examples and show numerical results.
PGMO Course 2013
December 4th and 11th, 2013, Ecole Polytechnique - "Sparse and robust optimization"
L. El Gahoui (U. Berkeley)
The course will report on recent results for decision under uncertainty under the robust optimization framework, and optimization in which the cardinality (number of non-zeros) of the decision variable is constrained. We will also review applications ranging from large-scale machine learning to energy management.