We look at solving mathematical programs that contain other optimization problems, specifically containing Optimal Value Functions (OVF). In general, problems with OVF are feature non-smoothness, that is both hard to model and solve. Rather than designing specific algorithms for this kind of problem, we propose an approach based on reformulations. In this talk we first focus the conditions for such reformulations to be applicable. Secondly, we present ReSHOP, an implementation of those procedures, as well as its Julia interface.
We introduce SELKIE, a general-purpose solver for equilibrium problems described by a set of agents. It exploits problem structures, such as block structure and cascading dependencies of interacting agents, in a flexible and adaptable way to achieve a more robust and faster solution path. Various decomposition schemes can be instantiated in a convenient and computationally efficient manner. SELKIE has been implemented and is available within GAMS/EMP. Examples illustrating the flexibility and effectiveness of SELKIE are given, including a Dantzig Wolfe method for Variational Inequalities.
joint work with Andy Philpott
Various countries have announced target dates for a 100% renewable electricity system. Such targets require long-term investment planning, medium-term storage management (including batteries and pumped storage), as well as a short-term analysis of demand-response, involuntary load curtailment and transmission congestion. We consider using complementarity models of dynamic risked equilibria to formulate these problems, the implications of stochasticity, and demonstrate the application of additional modeling constructs and distributed algorithms for their solution.