Tags » Convexity

Basic Notions Seminar is Back! Helly Type Theorems and the Cascade Conjecture

Kazhdan’s Basic Notion Seminar is back!

The “basic notion seminar” is an initiative of David Kazhdan who joined the Hebrew University math department  around 2000. People give series of lectures about basic mathematics (or not so basic at times). 753 more words

Combinatorics

Jensen's Inequality

The modern philosopher Nassim Nicholas Taleb says that one should never cross a river that is on average 4 feet deep. The intuition is clear: Averages are a borderline useless metric when the payoff structure (i.e. 187 more words

The Douglas-Rachford method for convex-concave saddle point problem without ever solving a linear system

Consider the saddle point problem

(where I omit all the standard assumptions, like convexity, continuity ans such…). Fenchel-Rockafellar duality says that solutions are characterized by the inclusion… 494 more words

Math

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. 731 more words
Variational Analysis

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. 352 more words

Variational Analysis

Moreau's identity for monotone operators

Here is a lemma that I find myself googling regularly since I always forget it’s exact form.

Lemma 1 Let be a monotone operator, and denote by the resolvent of .

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Math