# 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.