%
% File should contain your own tex definitions.
%

\newcommand{\theAdvisor}{Professor Michael C. Ferris}
\newcommand{\theTitle}{Algorithms and Environments for Complementarity}
\newcommand{\theAuthor}{Todd S. Munson}
\newcommand{\theDocType}{dissertation}
\newcommand{\theDepartment}{Computer Sciences}
\newcommand{\theDegree}{Doctor of Philosophy}

\newcommand{\partref}[1]{Part~\ref{part:#1}}
\newcommand{\chapref}[1]{Chapter~\ref{chap:#1}}
\newcommand{\secref}[1]{Section~\ref{sec:#1}}
\newcommand{\figref}[1]{Figure~\ref{fig:#1}}
\newcommand{\tabref}[1]{Table~\ref{tab:#1}}
\newcommand{\thmref}[1]{Theorem~\ref{thm:#1}}
\newcommand{\setref}[1]{(\ref{set:#1})}
\newcommand{\eqnref}[1]{(\ref{eqn:#1})}
\newcommand{\defref}[1]{Definition~\ref{def:#1}}

\newcommand{\norm}[1]{\left\| #1 \right\|}
\newcommand{\real}{\mathbf{R}}
\newcommand{\arcs}{\mathcal{A}}
\newcommand{\define}{:=}
\newcommand{\ie}{i.e.}
\newcommand{\defined}{:=}

\newcommand{\NCP}{NCP($F$)}
\newcommand{\VIP}{VIP$(X,F)$}
\renewcommand{\Re}{{\rm I}\!  {\rm R}}
\newcommand{\Ne}{{\rm I}\!  {\rm N}}
\newcommand{\rn}{\mathbf{R}^n}
\newcommand{\rntn}{\mathbf{R}^{n \times n}}
\newcommand{\eps}{\varepsilon}
\newcommand{\fa}{\frac{\partial \phi}{\partial a}}
\newcommand{\fb}{\frac{\partial \phi}{\partial b}}
\def\trt{^{\scriptscriptstyle T}}

\newtheorem{proposition}{Proposition}[section]
\newtheorem{theorem}[proposition]{Theorem}
\newtheorem{corollary}[proposition]{Corollary}
\newtheorem{lemma}[proposition]{Lemma}
\newtheorem{definition}[proposition]{Definition}
\newtheorem{assumption}[proposition]{Assumption}
\newtheorem{example}[proposition]{Example}
\newtheorem{algorithm}{Algorithm}{\bf}{\rm}

\newenvironment{mytable}{\begin{table}}{\end{table}}
\newenvironment{myfuncdef}{\begin{tabular}{p{5.6cm}p{5.3cm}}}{\end{tabular}}

\newenvironment{pf}
        {\begin{trivlist}\item[
        {\bf Proof }]}{\hfill\framebox[1.2ex]{\rule{0.3em}{0mm}} \end{trivlist}}

\newcommand{\maximize}{\operatornamewithlimits{maximize}}
\newcommand{\minimize}{\operatornamewithlimits{minimize}}
\newcommand{\diag}{\operatorname{diag}}
\newcommand{\rank}{\operatorname{rank}}
\newcommand{\argmin}{\operatornamewithlimits{arg\,min}}
\newcommand{\argmax}{\operatornamewithlimits{arg\,max}}
\newcommand{\sgn}{\operatorname{sgn}}

\newcommand{\natnum}{\operatorname{I}\!\operatorname{N}}
\newcommand{\oneto}[1]{1, \ldots , #1}
\newcommand{\map}[2]{#1 \mapsto #2}
\newcommand{\function}[3]{#1: #2 \to #3}
\newcommand{\plus}[1]{\left(#1 \right)_+}
\newcommand{\schur}[2]{\left(#1 \backslash #2\right)}

\newcommand{\ball}{\operatorname{I}\!\!\operatorname{B}}
\newcommand{\ip}[2]{\left\langle #1,#2 \right\rangle}
\newcommand{\modulus}[1]{\left| #1 \right|}
\newcommand{\seq}[1]{\left\{ #1 \right\}}
\newcommand{\set}[2]{\seq{#1 \,\colon\, #2}}

\newcommand{\proj}[2]{\pi_{#2} (#1)}
\newcommand{\perpspace}[1]{\left(#1\right)^{\perp}}
\newcommand{\intr}{\operatorname{int}}
\newcommand{\ri}{\operatorname{ri}}
\newcommand{\aff}{\operatorname{aff}}
\newcommand{\cl}{\operatorname{cl}}
\newcommand{\dom}{\operatorname{dom}}
\newcommand{\lin}{\operatorname{lin}}
\newcommand{\co}{\operatorname{co}}
\newcommand{\conv}{\operatorname{conv}}
\newcommand{\im}{\operatorname{im}}
\newcommand{\clco}{\overline{\operatorname{co}}}
\newcommand{\bdry}{\operatorname{bdry}}
\newcommand{\rec}{\operatorname{rec}}
\newcommand{\indicator}[2]{\psi_{#2} (#1)}
\newcommand{\indfn}[1]{\indicator{\cdot}{#1}}
\newcommand{\support}[2]{\conj{\psi_{#2}}\left(#1\right)}
\newcommand{\suppfn}[1]{\support{\cdot}{#1}}
\newcommand{\dist}[2]{\operatorname{dist}\left(#1 \mid #2\right)}
\newcommand{\distfn}[1]{\dist{\cdot}{#1}}
\newcommand{\ncone}[2]{N_{#2} \left(#1\right)}
\newcommand{\tcone}[2]{T_{#2}\left(#1\right)}
\newcommand{\contcone}[2]{K(#1 \mid #2)}
\newcommand{\pcone}[1]{{#1}^\circ}
\newcommand{\polar}[1]{{#1}^\circ}

\hyphenation{com-po-nent-wise}

\hyphenation{Lip-schitz}

\newcommand{\calA}{{\cal A}}
\newcommand{\calB}{{\cal B}}
\newcommand{\calC}{{\cal C}}
\newcommand{\calD}{{\cal D}}
\newcommand{\calE}{{\cal E}}
\newcommand{\calF}{{\cal F}}
\newcommand{\calH}{{\cal H}}
\newcommand{\calK}{{\cal K}}
\newcommand{\calL}{{\cal L}}
\newcommand{\calM}{{\cal M}}
\newcommand{\calN}{{\cal N}}
\newcommand{\calNC}{{\calN}_C}
\newcommand{\calNK}{{\calN}_K}
\newcommand{\calO}{{\cal O}}
\newcommand{\calP}{{\cal P}}
\newcommand{\xst}{x^*}
\newcommand{\barx}{\bar{x}}
\newcommand{\barw}{\bar{w}}
\newcommand{\barz}{\bar{z}}
\newcommand{\bart}{\bar{t}}
\newcommand{\barr}{\bar{r}}
\newcommand{\bargam}{\bar{\gamma}}
\newcommand{\barU}{\bar{U}}
\newcommand{\barV}{\bar{V}}
\newcommand{\xkp}{{x}^{k+1}}
\newcommand{\tkp}{{t}^{k+1}}
\newcommand{\xkd}{x'} %{{x}^{k}_{\dagger}}
\newcommand{\zkd}{z'} %{{x}^{k}_{\dagger}}
\newcommand{\tkd}{t'} %{{t}^{k}_{\dagger}}
\newcommand{\yjc}{x^\dagger} %{{x}^{k}_{\dagger}}
\newcommand{\sjc}{t^\dagger} %{{x}^{k}_{\dagger}}
\newcommand{\FC}{f_C}
\newcommand{\FR}{f_+}
\newcommand{\LFCk}{f_C}
\newcommand{\HC}{H_C}
\newcommand{\HR}{H_{+}}
\newcommand{\LH}{{\calL H}}
\newcommand{\LHk}{{\calL H}^k}
\newcommand{\LHC}{\calL\HC}
\newcommand{\LHR}{{\calL\HR}}
\newcommand{\LHCk}{{\calL\HC^k}}
\newcommand{\LLHCk}{{\calL\HC^k}}
\newcommand{\LHRk}{{\calL\HR^k}}
\newcommand{\p}{{P}}
\newcommand{\Lpk}{{\calL \p^k}}

\newcommand{\hata}{\hat{a}}
\newcommand{\hatc}{\hat{c}}
\newcommand{\hath}{\hat{h}}
\newcommand{\hatx}{\hat{x}}
\newcommand{\haty}{\hat{y}}
\newcommand{\xkdk}{\hat{x}^k}
\newcommand{\xkdkp}{\hat{x}^{k+1}}
\newcommand{\hats}{\hat{s}}
\newcommand{\hatt}{\hat{t}}
\newcommand{\hatw}{\hat{w}}
\newcommand{\hatz}{\hat{z}}
\newcommand{\hatH}{\hat{H}}
\newcommand{\hatHC}{\hat{H}_C}
\newcommand{\hk}{h^k}
\newcommand{\xk}{x^k}
\newcommand{\rk}{r^k}
\newcommand{\sk}{s^k}
\newcommand{\tk}{t^k}
\newcommand{\zk}{z^k}
\newcommand{\wk}{w^k}

\newcommand{\Jc}{J_{\rm c}}
\newcommand{\epsc}{\epsilon_{\rm c}}
\newcommand{\epst}{\epsilon_{\rm t}}
\newcommand{\epsf}{\epsilon_{f}}
\newcommand{\sigc}{\sigma{\rm c}}
\newcommand{\gamc}{\gamma_{\rm c}}
\newcommand{\hc}{h_{\rm c}}

\newcommand{\pic}[1]{\proj{#1}{C}}
%\newcommand{\pir}[1]{\proj{#1}{[l,u]}}
\newcommand{\pir}[1]{#1_+}
\newcommand{\compI}{{\backslash \cal I}}
\newcommand{\vareps}{\varepsilon}
\newcommand{\BalC}[1]{(\bar{x} + #1\ball)\cap C}

