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## Tags » Convexity

#### Sparse reconstruction with ℓ∞ constraints

Last week Christoph Brauer, Andreas Tillmann and myself uploaded the paper A Primal-Dual Homotopy Algorithm for -Minimization with -Constraints to the arXiv (and we missed being the first ever arXiv-paper with a non-trivial five-digit identifier by twenty-something papers…). 761 more words

#### Quasi Star (not Correlative) Convexity

Yesterday I published a post on a convexity-like concept here I learned about in this post. I’m going to copy my post below, with a couple additions, and a terminology change: what I there called -correlative convexity (-CC) I’m going to call here quasi star convexity (-QSC). 2,249 more words

#### Convergence of the iterates of the gradient method with constant stepsize

The gradient method with constant step length is the simplest method for solving unconstrained optimisation problems involving a continuously differentiable function with Lipschitz-continuous gradient. The motivation for this post came after reading this… 443 more words

#### Correlative (vs Quasi) Convexity

Update: See this updated post.

Playing around in the web I found this interesting post on stochastic gradient descent.

I haven’t fully absorbed the post, so I’m likely to write more. 1,732 more words

#### Pretty convexity result

Where here we discover some interesting facts about continuous convex functions.

We know that a function is convex if

for all and .

We see that if is a continuous function, then an equivalent condition for convexity is that either of the following inequalities holds 108 more words