Decomposition Approaches for Constrained Spatial Auction Market Problems

We consider several equilibrium formulations for the problem of managing spatially distributed auction markets of a homogeneous commodity, which are joined by transmission lines in a network. At each market, traders and buyers are determined by their price functions and choose their offer/bid values. We present equivalent variational inequality, optimization, and saddle point formulations of this problem. The corresponding models possess a special structure of constraint and cost functions and lead to different decomposition schemes. We propose proximal and splitting type methods and discuss their properties and preliminary computational results.