index.md

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Introduction

Welcome to the fmin.xyz - attempt to build intuitive systematic review of optimization theory, methods and applications. The initial goal of creating literature review for PhD thesis has transformed to the idea of something, that could be useful for people, making comparison of different optimizers easier and nice.

The site contains following parts:

• {% include link.html title="Theory"%}
• {% include link.html title="Methods"%}
• {% include link.html title="Exercises"%}
• {% include link.html title="Applications"%}

The site has 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 aims on researchers and enthisiasts 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 consist 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)