Cone programs and self-dual embeddings
This post aims at providing some intuition into cone programs from different perspectives; in particular:
- Equivalence of different formulations of cone programs
- Fenchel duality
- Primal-dual optimality conditions (OC)
- OCs as variational inequalities
- Homogeneous self-dual embeddings (HSDEs)
- OCs for HSDEs
Projection on the epigraph of the squared Euclidean norm
As a follow-up on the previous post titled Projection on an epigraph, we here discuss how we can project on the epigraph of the squared norm function. Continue reading →
Projection on an epigraph
Here we study the problem of projecting onto the epigraph of a convex continuous function. Unlike the computation of the proximal operator of a function or the projection on its sublevel sets, the projection onto epigraphs is more complex and there exist only a few functions for which semi-explicit formulas are available.
Projection of a point onto the epigraph of a convex function.
Mathematix 