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Introduction

Welcome to the fmin.xyz - an attempt to build an intuitive systematic review of optimization theory, methods, and applications.

The site contains the following parts:

The site has a simple built-in search 🔍. You can use it to find anything you want.

Rules of formatting and contributing could be found on the readme page on the github repo.

Principles

  • This site is aimed at researchers and enthusiasts with some prior expertise in the field (not just the Wikipedia clone).
  • The fundamental primitive structure of this site is the page.
  • The page should consists of short self-sufficient material about the topic.
  • If the page is based on paper, bibtex label should be added at the beginning.
  • The general structure of the site is flexible and should be improved over the time iteratively.

Notations and terms

These notations will be used by default (unless otherwise specified)

  • \(\theta\) – optimizing variable
  • \(\mathbb{R}^p\) – \(p\)-dimensional Euclidian space
  • \(\theta^*\) – global optimizer of the problem
  • \(\| \cdot \|\) – norm of the vector(matrix) (if nothing specified, we often use Euclidian (Frobenius) norm)
  • \(\| \cdot \|_*\) – dual norm (norm in dual space) (if nothing specified, we often use Euclidian (Frobenius) norm)