Preface

Skip to main content

\(\renewcommand{\glspostdescription}{} \def\cprime{\char"7E } \def\cdprime{\char"7F } \def\eoborotnoye{\char'013} \def\Eoborotnoye{\char'003} \newcommand{\beq}[1]{\begin{equation}\label{#1}} \newcommand{\eeq}{\end{equation}} \newcommand{\weakstar}{weak${}^*$ } \newcommand{\rng}{\operatorname{rng}} \newcommand{\ex}{\operatorname{ex}} \newcommand{\conv}{\operatorname{conv}} \newcommand{\cone}{\operatorname{cone}} \newcommand{\colex}{\prec_{\operatorname{colex}}} \newcommand{\lex}{\prec_{\operatorname{lex}}} \newcommand{\per}{\operatorname{per}} \newcommand{\permat}{\operatorname{pm}} \renewcommand{\hom}{\operatorname{hom}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\tr}{\operatorname{tr}} \newcommand{\tw}{\operatorname{tw}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\dist}{\operatorname{dist}} \newcommand{\degen}{\operatorname{degen}} \newcommand{\span}{\operatorname{span}} \newcommand{\sep}{\operatorname{sep}} \newcommand{\maxcut}{\operatorname{maxcut}} \newcommand{\degree}{d} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)

Preface Preface

The main focus of Discrete Optimization is on developing methods to find the “best” choice from among a finite (but usually astronomically large) set of options as quickly as possible. Such methods are widely applicable in practical applications such as resource allocation, scheduling, routing, assigning tasks, and beyond. Beyond these “industrial” applications, Discrete Optimization also provides a powerful toolkit for mathematical research in a wide range of areas. We will discuss some (simplified versions of) real world and research-related applications as they arise throughout the course.

While practical applications are certainly interesting and important, perhaps the greatest motivation for studying Discrete Optimization, especially for a pure mathematician (like the author), comes from the illuminating insights contained within it. Luckily, many of the most applicable ideas in this subject are also among the most stunning. My hope is that you will come away from this course with an appreciation of both the beauty and utility of Discrete Optimization.