## Tags » Convexity

#### 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

#### Convexity at 360learning.com: accelerated growth in a rational, and healthy work environment

360Learning is a startup dedicated to online learning for corporations, based on collaborative and social Learning Managment Software. 360Learning has implemented a very specific organization with its employees, that fosters accelerated growth while maintaing a rational and healthy work environment for its employees. 1,716 more words

Innovation

#### 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

Optimization

#### 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

Convergence

#### EC 23 HW - PART A - FOR AUG. 31

Please click the link below for the pdf.

Mathematical Economics

#### 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

Variational Analysis