Tag Archives: optimality conditions

Cone programs and self-dual embeddings

This post aims at providing some intuition into cone programs from different perspectives; in particular:

  1. Equivalence of different formulations of cone programs
  2. Fenchel duality
  3. Primal-dual optimality conditions (OC)
  4. OCs as variational inequalities
  5. Homogeneous self-dual embeddings (HSDEs)
  6. OCs for HSDEs

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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.

epiproj

Projection of a point onto the epigraph of a convex function.

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mathbabe

Exploring and venting about quantitative issues

Look at the corners!

The math blog of Dmitry Ostrovsky

The Unapologetic Mathematician

Mathematics for the interested outsider

Almost Sure

A random mathematical blog

Mathematix

Mathematix is the mathematician of the village of Asterix