Addressing Hierarchical Jointly-Convex Generalized Nash Equilibrium Problems with Nonsmooth Payoffs

We consider a Generalized Nash Equilibrium Problem whose joint feasible region is implicitly defined as the solution set of another Nash game. This structure arises e.g. in multi-portfolio selection contexts, whenever agents interact at different hierarchical levels. We consider nonsmooth terms in all players’ objectives, to promote, for example, sparsity in the solution. Under standard … Read more

Single-Forward-Step Projective Splitting: Exploiting Cocoercivity

This work describes a new variant of projective splitting for monotone inclusions, in which cocoercive operators can be processed with a single forward step per iteration. This result establishes a symmetry between projective splitting algorithms, the classical forward backward splitting method (FB), and Tseng’s forward-backward-forward method (FBF). Another symmetry is that the new procedure allows … Read more