$\newcommand{\eps}{\varepsilon} \newcommand{\kron}{\otimes} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\trace}{trace} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\minimize}{minimize} \DeclareMathOperator*{\maximize}{maximize} \DeclareMathOperator{\subjectto}{subject to} \newcommand{\mat}{\boldsymbol{#1}} \renewcommand{\vec}{\boldsymbol{\mathrm{#1}}} \newcommand{\vecalt}{\boldsymbol{#1}} \newcommand{\conj}{\overline{#1}} \newcommand{\normof}{\|#1\|} \newcommand{\onormof}{\|#1\|_{#2}} \newcommand{\MIN}{\begin{array}{ll} \minimize_{#1} & {#2} \end{array}} \newcommand{\MINone}{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\MINthree}{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \\ & {#4} \\ & {#5} \end{array}} \newcommand{\MAX}{\begin{array}{ll} \maximize_{#1} & {#2} \end{array}} \newcommand{\MAXone}{\begin{array}{ll} \maximize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\itr}{#1^{(#2)}} \newcommand{\itn}{^{(#1)}} \newcommand{\prob}{\mathbb{P}} \newcommand{\probof}{\prob\left\{ #1 \right\}} \newcommand{\pmat}{\begin{pmatrix} #1 \end{pmatrix}} \newcommand{\bmat}{\begin{bmatrix} #1 \end{bmatrix}} \newcommand{\spmat}{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} \newcommand{\sbmat}{\left[\begin{smallmatrix} #1 \end{smallmatrix}\right]} \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\eye}{\mat{I}} \newcommand{\mA}{\mat{A}} \newcommand{\mB}{\mat{B}} \newcommand{\mC}{\mat{C}} \newcommand{\mD}{\mat{D}} \newcommand{\mE}{\mat{E}} \newcommand{\mF}{\mat{F}} \newcommand{\mG}{\mat{G}} \newcommand{\mH}{\mat{H}} \newcommand{\mI}{\mat{I}} \newcommand{\mJ}{\mat{J}} \newcommand{\mK}{\mat{K}} \newcommand{\mL}{\mat{L}} \newcommand{\mM}{\mat{M}} \newcommand{\mN}{\mat{N}} \newcommand{\mO}{\mat{O}} \newcommand{\mP}{\mat{P}} \newcommand{\mQ}{\mat{Q}} \newcommand{\mR}{\mat{R}} \newcommand{\mS}{\mat{S}} \newcommand{\mT}{\mat{T}} \newcommand{\mU}{\mat{U}} \newcommand{\mV}{\mat{V}} \newcommand{\mW}{\mat{W}} \newcommand{\mX}{\mat{X}} \newcommand{\mY}{\mat{Y}} \newcommand{\mZ}{\mat{Z}} \newcommand{\mLambda}{\mat{\Lambda}} \newcommand{\mPbar}{\bar{\mP}} \newcommand{\ones}{\vec{e}} \newcommand{\va}{\vec{a}} \newcommand{\vb}{\vec{b}} \newcommand{\vc}{\vec{c}} \newcommand{\vd}{\vec{d}} \newcommand{\ve}{\vec{e}} \newcommand{\vf}{\vec{f}} \newcommand{\vg}{\vec{g}} \newcommand{\vh}{\vec{h}} \newcommand{\vi}{\vec{i}} \newcommand{\vj}{\vec{j}} \newcommand{\vk}{\vec{k}} \newcommand{\vl}{\vec{l}} \newcommand{\vm}{\vec{l}} \newcommand{\vn}{\vec{n}} \newcommand{\vo}{\vec{o}} \newcommand{\vp}{\vec{p}} \newcommand{\vq}{\vec{q}} \newcommand{\vr}{\vec{r}} \newcommand{\vs}{\vec{s}} \newcommand{\vt}{\vec{t}} \newcommand{\vu}{\vec{u}} \newcommand{\vv}{\vec{v}} \newcommand{\vw}{\vec{w}} \newcommand{\vx}{\vec{x}} \newcommand{\vy}{\vec{y}} \newcommand{\vz}{\vec{z}} \newcommand{\vpi}{\vecalt{\pi}} \newcommand{\vlambda}{\vecalt{\lambda}}$ # Computational methods in optimization

## Announcements

2020-03-26
Project details posted
2020-03-02
Homework 7 posted
2020-02-20
Homework 6 posted
2020-02-25
Homework 6 posted
2020-02-18
Homework 5 posted
2020-02-10
Homework 4 posted
2020-02-03
Homework 3 posted
2020-01-27
Homework 2 posted
2020-01-14
Homework 1 posted
2020-01-09
Please complete the intro survey by class on 2020-01-16 (submit on Gradescope)

## Overview

This course is a introduction to optimization for graduate students for those in any computational field.
It will cover many of the fundamentals of optimization and is a good course to prepare those who wish to use optimization in their research and those who wish to become optimizers by developing new algorithms and theory. Selected topics include:

• newton, quasi-newton, and trust region methods for unconstrained problems
• linear programming
• constrained least squares problems
• convex optimization

## Prerequisties

We'll assume you've had some background in numerical linear algebra and rely on that subject heavily. Students with a background in mathematical analysis may be able to appreciate some of the more theoretical results as well.