%%%%%%%%%%%%%%%%%% % LaTeX macros.tex % 27 Apr 2003: \def replaced by \newcommand % 17 Aug 2005: \Frac fixed (needs {} around #1 and #2). % \Newcommand, \pmat, \bmat introduced. % NB: \Newcommand doesn't work with commands that have [] arguments. % 05 Sep 2005: Added innerproduct % 08 Dec 2005: Realized that \providecommand already does what we were % trying to do with \Newcommand. % 11 Dec 2005: Revived \Newcommand to overload commands from other packages. % 13 Aug 2007: AF changed ``\mathrm'' to ``\operator@font'' %%%%%%%%%%%%%%%%%% \makeatletter %\newcommand{\proof{\penalty 25\noindent{\bf Proof.}\nobreak\hskip 1em\ignorespaces} %\newcommand{\emptybox}{\ \vbox{\hrule\hbox{\vrule height1.3ex\hskip0.8ex\vrule}\hrule}} \newcommand{\emptybox}{\vbox{\hrule height0.6pt\hbox{\vrule height1.3ex width0.6pt\hskip0.8ex% \vrule width0.6pt}\hrule height0.6pt}} % SIAM \endproof \newcommand{\noproof}{\hspace{.5em}\blackslug} \newcommand{\m}{\phantom-} \newcommand{\mm}[1]{\hbox{$#1$}} % math mode \newcommand{\mtx}[2]{\renewcommand{\arraystretch}{1.2}% \left(\! \begin{array}{#1}#2\end{array}\! \right)} % The next two are better than \mtx. \newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}} % Need \usepackage{amsmath} \newcommand{\bmat}[1]{\begin{bmatrix}#1\end{bmatrix}} % Does anyone know how to do this with \newcommand? \ifx \innerprod\undefined% \def\innerprod(#1,#2){\langle#1,#2\rangle} % Must be called as \innerproduct(A,B) \fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Replace commands defined in other packages%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\Newcommand}[2]% {\ifx#1\undefined \newcommand{#1}{#2} \else \renewcommand{#1}{#2} \fi} \ifx\mod\undefined \newcommand{\mod}[1]{|#1|} \else \renewcommand{\mod}[1]{|#1|} \fi \ifx\Range\undefined \newcommand{\Range}{\mathop{\operator@font{range}}} \else \renewcommand{\Range}{\mathop{\operator@font{range}}} \fi \Newcommand{\Re} {\mathbb{R}} % Need \usepackage{amssymb} \Newcommand{\subject} {\hbox{\rm subject to}} % Need \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Commands defined in other packages%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \providecommand{\det} {\mathop{\operator@font{det}}} \providecommand{\diag} {\mathop{\operator@font{diag}}} \providecommand{\dim} {\mathop{\operator@font{dim}}} \providecommand{\exp} {\mathop{\operator@font{exp}}} \providecommand{\Frac}[2]{{\textstyle{\frac{#1}{#2}}}} %\providecommand{\mod}[1]{|#1|} \providecommand{\rank} {\mathop{\operator@font{rank}}} %\providecommand{\Re} {\mathbb{R}} % Need \usepackage{amssymb} \providecommand{\Co} {\mathbb{C}} % Need \usepackage{amssymb} \providecommand{\vec} {\mathop{\operator@font{vec}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\st}{:} \newcommand{\abs}[1]{|#1|} \newcommand{\argmin}{\mathop{\operator@font{argmin}}} \newcommand{\argmax}{\mathop{\operator@font{argmax}}} \newcommand{\conv}{\mathop{\operator@font{conv}}} \newcommand{\eig}{\mathop{\operator@font{eig}}} \newcommand{\mv}[1]{\mathtt{#1}} \newcommand{\mtt}[1]{\mathtt{#1}} \newcommand{\T}{^T\!} \newcommand{\Tinv}{^{-T}\!} \newcommand{\und}[1]{$\underline{\hbox{#1}}$} \newcommand{\gge}{\succeq} \newcommand{\twonorm}[1]{\norm{#1}_2} \newcommand{\onenorm}[1]{\norm{#1}_1} \newcommand{\infnorm}[1]{\norm{#1}_{\infty}} \newcommand{\dualnorm}[1]{\norm{#1}_D} \newcommand{\disp}{\displaystyle} \newcommand{\super}{\scriptstyle} \newcommand{\superplus}{^{+}} \newcommand{\superminus}{^{-}} \newcommand{\ur}{\mbox{\bf u}} %\newcommand{\Re}{I\!\!R} \newcommand{\sgap}{\;} \newcommand{\mgap}{\;\;} \newcommand{\bgap}{\;\;\;} %\newcommand{\subject}{\hbox{\rm subject to}} \newcommand{\minimize}[1]{{\displaystyle\minim_{#1}}} \newcommand{\minimizearg}[2]{{\displaystyle\minim_{#1 \in \Re^{#2}}}} \newcommand{\maximizearg}[2]{{\displaystyle\maxim_{#1 \in \Re^{#2}}}} \newcommand{\minimizetwoarg}[4]{{\displaystyle\minim_{#1 \in \Re^{#2},% #3 \in \Re^{#4}}}} \newcommand{\maximizetwoarg}[4]{{\displaystyle\maxim_{#1 \in \Re^{#2},% #3 \in \Re^{#4}}}} \newcommand{\maximize}[1]{{\displaystyle\maxim_{#1}}} \newcommand{\eval}[2]{\left.#1\right|_{\alpha=#2}} % alpha suffix \newcommand{\evaluate}[2]{\left.#1\right|_{#2}} % arbitrary suffix \newcommand{\Bigp}[1]{\bigl(#1\bigr)} \newcommand{\tmat}[2]{(\, #1 \ \ #2 \,)} \newcommand{\tmatt}[3]{(\, #1 \ \ #2 \ \ #3\,)} \newcommand{\tmattt}[4]{(\, #1 \ \ #2 \ \ #3 \ \ #4\,)} \newcommand{\tmatttt}[5]{(\, #1 \ \ #2 \ \ #3 \ \ #4 \ \ #5\,)} \newcommand{\mat}[2]{\Bigp{\; #1 \quad #2 \;}} \newcommand{\matt}[3]{\Bigp{\; #1 \quad #2 \quad #3\;}} \newcommand{\mattt}[4]{\Bigp{\; #1 \quad #2 \quad #3 \quad #4\;}} \newcommand{\matttt}[5]{\Bigp{\; #1 \quad #2 \quad #3 \quad #4 \quad #5\;}} \newcommand{\Cpp}{C\raise3pt\hbox{\tiny++}} \newcommand{\blackslug}{\hbox{\hskip 1pt \vrule width 4pt height 6pt depth 1.5pt \hskip 1pt}} \newcommand{\boxit}[1]{\vbox{\hrule\hbox{\vrule\hskip 3pt \vbox{\vskip 3pt #1 \vskip 3pt}\hskip 3pt\vrule}\hrule}} \newcommand{\cross}{\scriptscriptstyle\times} \newcommand{\maxim}{\mathop{\operator@font{maximize}}} \newcommand{\minim}{\mathop{\operator@font{minimize}}} \newcommand{\cond}{\mathop{\operator@font{cond}}} \newcommand{\defined}{\buildrel{\scriptscriptstyle\triangle}\over=} \newcommand{\definedas}{\defined} \newcommand{\sep}{\mathop{\operator@font{sep}}} \newcommand{\In}{\mathop{\operator@font{In}}} \newcommand{\boundary}{\mathop{\operator@font{bnd}}} \newcommand{\interior}{\mathop{\operator@font{int}}} \newcommand{\Null}{\mathop{\operator@font{null}}} \newcommand{\Rank}{\mathop{\operator@font{rank}}} \newcommand{\op}{\mathop{\operator@font{op}}} \newcommand{\re}{\mathop{\operator@font{re}}} \newcommand{\range}{\mathop{\operator@font{range}}} \newcommand{\sign}{\mathop{\operator@font{sign}}} \newcommand{\sgn}{\mathop{\operator@font{sgn}}} %\newcommand{\Span}{\mbox{\rm span}} \newcommand{\Span}{\mathop{\operator@font{span}}} \newcommand{\trace}{\mathop{\operator@font{trace}}} \newcommand{\drop}{^{\null}} \newcommand{\etal}{et al.} %%% No italics!! Also, must say \etal\ \newcommand{\float}{fl} \newcommand{\Grad}{\nabla\!} %\newcommand{\grad}{\nabla} % Already defined \newcommand{\Hess}{\nabla^2\!} \newcommand{\half} {{\textstyle\frac12}} \newcommand{\third} {{\textstyle\frac13}} \newcommand{\fourth}{{\textstyle\frac14}} \newcommand{\sixth}{{\textstyle\frac16}} \newcommand{\eighth}{{\textstyle\frac18}} \newcommand{\inv}{^{-1}} \newcommand{\invsq}{^{-2}} \newcommand{\limk}{\lim_{k\to\infty}} \newcommand{\modd}[1]{\biggl|#1\biggr|} \newcommand{\Mod}[1]{\left|#1\right|} \newcommand{\normm}[1]{\biggl\|#1\biggr\|} \newcommand{\norm}[1]{\|#1\|} \newcommand{\pinv}{^\dag} % pseudoinverse \newcommand{\seql}[2]{\{\hthinsp#1\hthinsp\}_{#2}} \newcommand{\seq}[1]{\seql{#1}{k\ge0}} \newcommand{\Seq}[1]{\{\hthinsp#1\hthinsp\}} \newcommand{\Set}[1]{\{\, #1 \,\}} \newcommand{\spose}[1]{\hbox to 0pt{#1\hss}} \newcommand{\sub}[1]{^{\null}_{#1}} \newcommand{\till}{\,{:}\,} % Matlab i = 1:n as i = 1\till n \newcommand{\lwords}[1]{\text{#1}\mgap} % text automatically adjusts the size \newcommand{\rwords}[1]{\mgap\text{#1}} \newcommand{\lwordss}[1]{\text{#1}\quad} % text automatically adjusts the size \newcommand{\rwordss}[1]{\quad\text{#1}} \newcommand{\lwordsss}[1]{\text{#1}\qquad} % text automatically adjusts the size \newcommand{\rwordsss}[1]{\qquad\text{#1}} \newcommand{\words}[1]{\mgap\text{#1}\mgap} \newcommand{\wordss}[1]{\quad\text{#1}\quad} \newcommand{\wordsss}[1]{\qquad\text{#1}\qquad} \newcommand{\xint}{{x_{\rm int}}} %%% Fixed-size glue, only for math mode \newcommand{\hthinsp}{\mskip 1 mu} % thin space \newcommand{\pthinsp}{\mskip 2 mu} % thin space \newcommand{\pmedsp }{\mskip 2.75mu} % medium space \newcommand{\pthiksp}{\mskip 3.5 mu} % thick space \newcommand{\nthinsp}{\mskip -2 mu} \newcommand{\nmedsp }{\mskip -2.75mu} \newcommand{\nthiksp}{\mskip -3.5 mu} %%% Specially lowered subscripts (see \sub above) \newcommand{\Asubk}{A\sub{\nthinsp k}} \newcommand{\Bsubk}{B\sub{\nthinsp k}} \newcommand{\Fsubk}{F\sub{\nmedsp k}} \newcommand{\Gsubk}{G\sub{\nthinsp k}} \newcommand{\Hsubk}{H\sub{\nthinsp k}} \newcommand{\HsubB}{H\sub{\nthinsp\scriptscriptstyle{B}}} \newcommand{\HsubS}{H\sub{\nthinsp\scriptscriptstyle{S}}} \newcommand{\HsubBS}{H\sub{\nthinsp\scriptscriptstyle\mathit{BS}}} \newcommand{\Hz}{H\sub{\nthinsp \scriptscriptstyle{Z}}} \newcommand{\Jsubk}{J\sub{\nmedsp k}} \newcommand{\Psubk}{P\sub{\nthiksp k}} \newcommand{\Qsubk}{Q\sub{\nthinsp k}} \newcommand{\Vsubk}{V\sub{\nmedsp k}} \newcommand{\Vsubone}{V\sub{\nmedsp 1}} \newcommand{\Vsubtwo}{V\sub{\nmedsp 2}} \newcommand{\Ysubk}{Y\sub{\nmedsp k}} \newcommand{\Wsubk}{W\sub{\nthiksp k}} \newcommand{\Zsubk}{Z\sub{\nthinsp k}} \newcommand{\Zsubi}{Z\sub{\nthinsp i}} %%% Subscripts \newcommand{\subfr}{_{\scriptscriptstyle\mathit{FR}}} \newcommand{\subfx}{_{\scriptscriptstyle\mathit{FX}}} \newcommand{\fr}{\subfr} \newcommand{\fx}{\subfx} \newcommand{\submax}{_{\max}} \newcommand{\submin}{_{\min}} \newcommand{\subminus}{_{\scriptscriptstyle -}} \newcommand{\subplus }{_{\scriptscriptstyle +}} \newcommand{\A}{_{\scriptscriptstyle A}} \newcommand{\B}{_{\scriptscriptstyle B}} %\newcommand{\BS}{_{\scriptscriptstyle BS}} \newcommand{\C}{_{\scriptscriptstyle C}} \newcommand{\D}{_{\scriptscriptstyle D}} \newcommand{\E}{_{\scriptscriptstyle E}} \newcommand{\F}{_{\scriptscriptstyle F}} \newcommand{\G}{_{\scriptscriptstyle G}} \newcommand{\I}{_{\scriptscriptstyle I}} \newcommand{\w}{_w} %\newcommand{\k}{_k} \newcommand{\kp}[1]{_{k+#1}} \newcommand{\km}[1]{_{k-#1}} %\newcommand{\j}{_j} \newcommand{\jp}[1]{_{j+#1}} \newcommand{\jm}[1]{_{j-#1}} %\newcommand{\i}{_i} \newcommand{\ip}[1]{_{i+#1}} \newcommand{\im}[1]{_{i-#1}} \newcommand{\K}{_{\scriptscriptstyle K}} \renewcommand{\L}{_{\scriptscriptstyle L}} \newcommand{\M}{_{\scriptscriptstyle M}} \newcommand{\N}{_{\scriptscriptstyle N}} %\newcommand{\subb}{\B} %\newcommand{\subc}{\C} %\newcommand{\subm}{\M} %\newcommand{\subf}{\F} %\newcommand{\subn}{\N} %\newcommand{\subh}{\H} %\newcommand{\subk}{\K} %\newcommand{\subt}{_{\scriptscriptstyle T}} %\newcommand{\subr}{\R} %\newcommand{\subz}{\Z} \newcommand{\J}{_{\scriptscriptstyle J}} %\newcommand{\O}{_{\scriptscriptstyle O}} \renewcommand{\P}{_{\scriptscriptstyle P}} \newcommand{\Q}{_{\scriptscriptstyle Q}} %\newcommand{\R}{_{\scriptscriptstyle R}} \let\Sec=\S \renewcommand{\S}{_{\scriptscriptstyle S}} \renewcommand{\N}{_{\scriptscriptstyle N}} \Newcommand{\R}{_{\scriptscriptstyle R}} \newcommand{\U}{_{\scriptscriptstyle U}} \newcommand{\V}{_{\scriptscriptstyle V}} \newcommand{\W}{_{\scriptscriptstyle W}} \newcommand{\X}{_{\scriptscriptstyle X}} \newcommand{\Y}{_{\scriptscriptstyle Y}} \newcommand{\Z}{_{\scriptscriptstyle Z}} %%% Superscript stars \newcommand{\starsymbol}{\ast} \newcommand{\superstar}{^\starsymbol} \newcommand{\starT}{\starsymbol T\!} \newcommand{\starTT}{\starsymbol T} \newcommand{\SUPERSTAR}{^{\raise 0.5pt\hbox{$\starsymbol$}}} \renewcommand{\SUPERSTAR}{\superstar} \newcommand{\shrink}{\mskip -7mu} %%% Less space after \xstar if followed by , or . \newcommand{\alphastar}{\alpha\superstar} \newcommand{\sigmastar}{\sigma\superstar} \newcommand{\gammastar}{\gamma\superstar} \newcommand{\lamstar }{\lambda\superstar} \newcommand{\lamstarT}{\lambda^{\starT}} \newcommand{\lambdastar}{\lamstar} \newcommand{\nustar}{\nu\superstar} \newcommand{\mustar}{\mu\superstar} \newcommand{\pistar}{\pi\superstar} \newcommand{\thetastar}{\theta\superstar} \newcommand{\cstar}{c\superstar} \newcommand{\dstar}{d\superstar} \newcommand{\fstar}{f\superstar} \newcommand{\gstar}{g\superstar} \newcommand{\hstar}{h\superstar} \newcommand{\mstar}{m\superstar} \newcommand{\pstar}{p\superstar} \newcommand{\sstar}{s\superstar} \newcommand{\ustar}{u\superstar} \newcommand{\vstar}{v\superstar} \newcommand{\wstar}{w\superstar} \newcommand{\xstar}{x\superstar} \newcommand{\ystar}{y\superstar} \newcommand{\zstar}{z\superstar} \newcommand{\Astar}{A\SUPERSTAR} \newcommand{\Bstar}{B\SUPERSTAR} \newcommand{\Cstar}{C\SUPERSTAR} \newcommand{\Fstar}{F\SUPERSTAR} \newcommand{\Gstar}{G\SUPERSTAR} \newcommand{\Hstar}{H\SUPERSTAR} \newcommand{\Jstar}{J\SUPERSTAR} \newcommand{\Kstar}{K\SUPERSTAR} \newcommand{\Mstar}{M\SUPERSTAR} \newcommand{\Qstar}{Q\SUPERSTAR} \newcommand{\Ustar}{U\SUPERSTAR} \newcommand{\Vstar}{V\SUPERSTAR} \newcommand{\Wstar}{W\SUPERSTAR} \newcommand{\Xstar}{X\SUPERSTAR} \newcommand{\Zstar}{Z\SUPERSTAR} %%% bars, hats, tildes (\skew4 is the default) \newcommand{\alphabar}{\skew3\bar\alpha} \newcommand{\alphahat}{\skew3\hat\alpha} \newcommand{\alphatilde}{\skew3\tilde\alpha} \newcommand{\betabar}{\skew{2.8}\bar\beta} %\newcommand{\betahat}{\skew{2.8}\widehat\beta} \newcommand{\betahat}{\skew6\hat\beta} \newcommand{\betatilde}{\skew6\tilde\beta} \newcommand{\delbar}{\bar\delta} \newcommand{\deltilde}{\skew5\tilde\delta} \newcommand{\deltabar}{\delbar} \newcommand{\deltatilde}{\deltilde} \newcommand{\epsbar}{\skew3\bar\epsilon} \newcommand{\lambar}{\bar\lambda} \newcommand{\etabar}{\bar\eta} \newcommand{\etahat}{\hat\eta} \newcommand{\gammabar}{\bar\gamma} %\newcommand{\lamhat}{\skew{2.8}\widehat\lambda} %\newcommand{\lamhat}{\skew{3.8}\widehat\lambda} \newcommand{\lamhat}{\widehat\lambda} \newcommand{\lamtilde}{\widetilde\lambda} \newcommand{\lambdabar}{\lambar} \newcommand{\lambdahat}{\lamhat} \newcommand{\mubar}{\skew3\bar \mu} \newcommand{\muhat}{\skew3\widehat \mu} \newcommand{\mutilde}{\widetilde\mu} \newcommand{\nubar}{\skew3\bar\nu} \newcommand{\nuhat}{\skew3\widehat\nu} \newcommand{\nutilde}{\skew3\tilde\nu} \newcommand{\omegabar}{\bar\omega} \newcommand{\varphihat}{\widehat\varphi} \newcommand{\varphibar}{\bar\varphi} \newcommand{\pibar}{\skew1\bar\pi} \newcommand{\pihat}{\skew1\widehat \pi} \newcommand{\sigmabar}{\skew{2.8}\bar\sigma} \newcommand{\sigmahat}{\skew3\hat\sigma} %\newcommand{\sigmahat}{\widehat\sigma} \newcommand{\sigmatilde}{\skew{2.8}\tilde\sigma} \newcommand{\rhobar}{\bar\rho} %\newcommand{\rhohat}{\skew2\widehat\rho} \newcommand{\rhohat}{\skew{3.5}\hat\rho} \newcommand{\taubar}{\bar\tau} \newcommand{\tautilde}{\tilde\tau} \newcommand{\tauhat}{\widehat\tau} \newcommand{\thetabar}{\bar\theta} \newcommand{\thetahat}{\hat\theta} \newcommand{\xibar}{\skew4\bar\xi} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Math italic and calligraphic fonts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \providecommand{\varGamma} {{\mathit\Gamma}} \providecommand{\varDelta} {{\mathit\Delta}} \providecommand{\varTheta} {{\mathit\Theta}} \providecommand{\varLambda} {{\mathit\Lambda}} \providecommand{\varXi} {{\mathit\Xi}} \providecommand{\varPi} {{\mathit\Pi}} \providecommand{\varSigma} {{\mathit\Sigma}} \providecommand{\varUpsilon}{{\mathit\Upsilon}} \providecommand{\varPhi} {{\mathit\Phi}} \providecommand{\varPsi} {{\mathit\Psi}} \providecommand{\varOmega} {{\mathit\Omega}} \newcommand{\Deltait}{\varDelta} \newcommand{\Gammait}{\varGamma} \newcommand{\Gammabarit}{\skew5\bar\Gammait} \newcommand{\Lambdait}{\varLambda} \newcommand{\Lamhatit}{\skew5\widehat\Lambdait} \newcommand{\Lambarit}{\skew5\bar\Lambdait} \newcommand{\Omegait}{\varOmega} \newcommand{\Omegaitbar}{\skew5\bar\Omegait} \newcommand{\Piit}{\varPi} \newcommand{\Pibarit}{\bar\varPi} \newcommand{\Pihatit}{\skew5\widehat\varPi} \newcommand{\Piitbar}{\skew5\bar\Piit} \newcommand{\Phiit}{\varPhi} \newcommand{\Psiit}{\varPsi} \newcommand{\Sigmait}{\varSigma} \newcommand{\Thetait}{\varTheta} \newcommand{\Upsilonit}{\varUpsilon} \newcommand{\Xiit}{\varXi} \newcommand{\setA}{\mathcal{A}} \newcommand{\setB}{\mathcal{B}} \newcommand{\setC}{\mathcal{C}} \newcommand{\setD}{\mathcal{D}} \newcommand{\setE}{\mathcal{E}} \newcommand{\setF}{\mathcal{F}} \newcommand{\setG}{\mathcal{G}} \newcommand{\setI}{\mathcal{I}} \newcommand{\setJ}{\mathcal{J}} \newcommand{\setM}{\mathcal{M}} \newcommand{\setP}{\mathcal{P}} \newcommand{\setS}{\mathcal{S}} \newcommand{\setU}{\mathcal{U}} \newcommand{\setV}{\mathcal{V}} \newcommand{\setW}{\mathcal{W}} \newcommand{\setX}{\mathcal{X}} \newcommand{\suba}{_a} \newcommand{\subb}{_b} \newcommand{\subc}{_c} \newcommand{\sube}{_e} \newcommand{\subf}{_f} \newcommand{\subi}{_i} \newcommand{\subm}{_m} \newcommand{\subr}{_r} \newcommand{\subs}{_s} \newcommand{\subv}{_v} \newcommand{\subw}{_w} \newcommand{\subz}{_z} \newcommand{\subA}{_{\scriptscriptstyle A}} \newcommand{\subB}{_{\scriptscriptstyle B}} \newcommand{\subC}{_{\scriptscriptstyle C}} \newcommand{\subE}{_{\scriptscriptstyle E}} \newcommand{\subF}{_{\scriptscriptstyle F}} \newcommand{\subI}{_{\scriptscriptstyle I}} \newcommand{\subM}{_{\scriptscriptstyle M}} \newcommand{\subg}{_{\scriptscriptstyle G}} \newcommand{\subl}{_{\scriptscriptstyle L}} \newcommand{\subn}{_{\scriptscriptstyle N}} \newcommand{\subh}{_{\scriptscriptstyle H}} \newcommand{\subk}{_{\scriptscriptstyle K}} \newcommand{\subt}{_{\scriptscriptstyle T}} \newcommand{\subp}{_{\scriptscriptstyle P}} \newcommand{\subq}{_{\scriptscriptstyle Q}} \newcommand{\subR}{_{\scriptscriptstyle R}} \newcommand{\subS}{_{\scriptscriptstyle S}} \newcommand{\subV}{_{\scriptscriptstyle V}} \newcommand{\subW}{_{\scriptscriptstyle W}} \newcommand{\subZ}{_{\scriptscriptstyle Z}} \newcommand{\Ascr}{{\mathcal A}} \newcommand{\Bscr}{{\mathcal B}} \newcommand{\Cscr}{{\mathcal C}} \newcommand{\Fscr}{{\mathcal F}} \newcommand{\Dscr}{{\mathcal D}} \newcommand{\Gscr}{{\mathcal G}} \newcommand{\Gscrbar}{{\mathcal\Gbar}} \newcommand{\Hscr}{{\mathcal H}} \newcommand{\Iscr}{{\mathcal I}} \newcommand{\Jscr}{{\mathcal J}} \newcommand{\Kscr}{{\mathcal K}} \newcommand{\Kscrbar}{{\mathcal\Kbar}} \newcommand{\Lscr}{{\mathcal L}} \newcommand{\Mscr}{{\mathcal M}} \newcommand{\lscr}{\ell} \newcommand{\lscrbar}{\ellbar} \newcommand{\Oscr}{{\mathcal O}} \newcommand{\Pscr}{{\mathcal P}} \newcommand{\Qscr}{{\mathcal Q}} \newcommand{\Sscr}{{\mathcal S}} \newcommand{\Tscr}{{\mathcal T}} \newcommand{\Uscr}{{\mathcal U}} \newcommand{\Vscr}{{\mathcal V}} \newcommand{\Wscr}{{\mathcal W}} %\newcommand{\Mscr}{{\mathcal M}} \newcommand{\Nscr}{{\mathcal N}} \newcommand{\Rscr}{{\mathcal R}} \newcommand{\Xscr}{{\mathcal X}} \newcommand{\abar}{\skew3\bar a} \newcommand{\ahat}{\skew2\widehat a} \newcommand{\atilde}{\skew2\widetilde a} \newcommand{\Abar}{\skew7\bar A} \newcommand{\Ahat}{\widehat A} \newcommand{\Atilde}{\widetilde A} \newcommand{\bbar}{\skew3\bar b} \newcommand{\bhat}{\skew2\widehat b} \newcommand{\btilde}{\skew2\widetilde b} \newcommand{\Bbar}{\bar B} \newcommand{\Bhat}{\skew4\widehat B} \newcommand{\Btilde}{\skew4\widetilde B} \newcommand{\cbar}{\skew5\bar c} \newcommand{\chat}{\skew3\widehat c} \newcommand{\ctilde}{\widetilde c} \newcommand{\Cbar}{\bar C} \newcommand{\Chat}{\widehat C} \newcommand{\Ctilde}{\widetilde C} \newcommand{\dbar}{\bar d} \newcommand{\dhat}{\widehat d} \newcommand{\dtilde}{\widetilde d} \newcommand{\Dbar}{\bar D} \newcommand{\Dhat}{\widehat D} \newcommand{\Dtilde}{\widetilde D} \newcommand{\ehat}{\skew3\widehat e} \newcommand{\ebar}{\bar e} \newcommand{\Ebar}{\bar E} \newcommand{\Ehat}{\widehat E} \newcommand{\fbar}{\bar f} \newcommand{\fhat}{\widehat f} \newcommand{\ftilde}{\widetilde f} \newcommand{\Fbar}{\bar F} \newcommand{\Fhat}{\widehat F} \newcommand{\gbar}{\skew{4.3}\bar g} %\newcommand{\ghat}{\skew{4.3}\widehat g} \newcommand{\ghat}{\skew{4.3}\hat g} \newcommand{\gtilde}{\skew{4.5}\widetilde g} \newcommand{\Gbar}{\bar G} \newcommand{\Ghat}{\widehat G} %\newcommand{\hbar}{\skew{4.2}\bar h} \newcommand{\hhat}{\skew2\widehat h} \newcommand{\htilde}{\skew3\widetilde h} \newcommand{\Hbar}{\skew5\bar H} \newcommand{\Hhat}{\widehat H} \newcommand{\Htilde}{\widetilde H} \newcommand{\Ibar}{\skew5\bar I} \newcommand{\Itilde}{\widetilde I} \newcommand{\Jbar}{\skew6\bar J} \newcommand{\Jhat}{\widehat J} \newcommand{\Jtilde}{\widetilde J} \newcommand{\kbar}{\skew{4.4}\bar k} \newcommand{\Khat}{\widehat K} \newcommand{\Kbar}{\skew{4.4}\bar K} \newcommand{\Ktilde}{\widetilde K} \newcommand{\ellbar}{\bar \ell} \newcommand{\lhat}{\skew2\widehat l} \newcommand{\lbar}{\skew2\bar l} \newcommand{\Lbar}{\skew{4.3}\bar L} \newcommand{\Lhat}{\widehat L} \newcommand{\Ltilde}{\widetilde L} \newcommand{\mbar}{\skew2\bar m} \newcommand{\mhat}{\widehat m} \newcommand{\mtilde}{\widetilde m} \newcommand{\Mbar}{\skew{4.4}\bar M} %\newcommand{\Mhat}{\widehat M} % too wide!! \newcommand{\Mhat}{\skew4\hat M} \newcommand{\Mtilde}{\widetilde M} \newcommand{\Nbar}{\skew{4.4}\bar N} \newcommand{\Ntilde}{\widetilde N} \newcommand{\nbar}{\skew2\bar n} \newcommand{\pbar}{\skew2\bar p} %\newcommand{\phat}{\skew2\widehat p} \newcommand{\phat}{\skew2\hat p} \newcommand{\ptilde}{\skew2\widetilde p} \newcommand{\Pbar}{\skew5\bar P} \newcommand{\Phat}{\widehat P} \newcommand{\Ptilde}{\skew5\widetilde P} \newcommand{\qbar}{\bar q} \newcommand{\qhat}{\skew2\widehat q} \newcommand{\qtilde}{\widetilde q} \newcommand{\Qbar}{\bar Q} \newcommand{\Qhat}{\widehat Q} \newcommand{\Qtilde}{\widetilde Q} \newcommand{\rbar}{\skew3\bar r} \newcommand{\rhat}{\skew3\widehat r} \newcommand{\rtilde}{\skew3\widetilde r} \newcommand{\Rbar}{\skew5\bar R} \newcommand{\Rhat}{\widehat R} \newcommand{\Rtilde}{\widetilde R} \newcommand{\sbar}{\bar s} %\newcommand{\shat}{\widehat s} \newcommand{\shat}{\skew3\hat s} \newcommand{\Stilde}{\widetilde S} \newcommand{\stilde}{\widetilde s} \newcommand{\Shat}{\widehat S} \newcommand{\Sbar}{\skew2\bar S} \newcommand{\tbar}{\bar t} \newcommand{\ttilde}{\widetilde t} \newcommand{\that}{\widehat t} \newcommand{\Tbar}{\bar T} \newcommand{\That}{\widehat T} \newcommand{\Ttilde}{\widetilde T} \newcommand{\ubar}{\skew3\bar u} \newcommand{\uhat}{\skew3\widehat u} \newcommand{\utilde}{\skew3\tilde u} \newcommand{\Ubar}{\skew2\bar U} \newcommand{\Uhat}{\widehat U} \newcommand{\Utilde}{\widetilde U} \newcommand{\vbar}{\skew3\bar v} \newcommand{\vhat}{\skew3\widehat v} \newcommand{\vtilde}{\skew3\widetilde v} \newcommand{\Vbar}{\skew2\bar V} \newcommand{\Vhat}{\widehat V} \newcommand{\Vtilde}{\widetilde V} \newcommand{\wbar}{\skew3\bar w} \newcommand{\what}{\skew3\widehat w} \newcommand{\wtilde}{\skew3\widetilde w} \newcommand{\Wbar}{\skew3\bar W} \newcommand{\What}{\widehat W} \newcommand{\Wtilde}{\widetilde W} \newcommand{\xbar}{\skew{2.8}\bar x} \newcommand{\xhat}{\skew{2.8}\widehat x} \newcommand{\xtilde}{\skew3\widetilde x} \newcommand{\Xhat}{\widehat X} \newcommand{\ybar}{\skew3\bar y} \newcommand{\yhat}{\skew3\widehat y} \newcommand{\ytilde}{\skew3\widetilde y} \newcommand{\Ytilde}{\widetilde Y} \newcommand{\Ybar}{\skew2\bar Y} \newcommand{\Yhat}{\widehat Y} \newcommand{\zbar}{\skew{2.8}\bar z} \newcommand{\zhat}{\skew{2.8}\widehat z} \newcommand{\ztilde}{\skew{2.8}\widetilde z} \newcommand{\Zbar}{\skew5\bar Z} \newcommand{\Zhat}{\widehat Z} \newcommand{\Ztilde}{\widetilde Z} \newcommand{\cf}{\textrm{cf.}} \providecommand{\Matlab}{{\sc Matlab}} \providecommand{\Gams }{{\sc Gams}} \providecommand{\Ampl }{{\sc Ampl}} \providecommand{\Nag }{{\sc Nag}} \providecommand{\Neos }{{\sc Neos}} \providecommand{\NAG }{{\small Nag}} \providecommand{\AMPL }{{\small AMPL}} \providecommand{\CUTE }{{\small CUTE}} \providecommand{\CUTEr }{{\small CUTE}r} \providecommand{\GAMS }{{\small GAMS}} \providecommand{\Knossos} {{\small K}nossos} \providecommand{\LANCELOT}{{\small LANCELOT}} \providecommand{\LPOPT }{{\small LPOPT}} \providecommand{\LSSOL }{{\small LSSOL}} \providecommand{\LUSOL }{{\small LUSOL}} \providecommand{\MINOS }{{\small MINOS}} \providecommand{\NLSSOL}{{\small NLSSOL}} \providecommand{\NPSOL }{{\small NPSOL}} \providecommand{\QPOPT }{{\small QPOPT}} \providecommand{\QPSOL }{{\small QPSOL}} \providecommand{\SNOPT }{{\small SNOPT}} \providecommand{\SNOPTA}{{\small SNOPTA}} \providecommand{\SNOPTB}{{\small SNOPTB}} \providecommand{\SQOPT }{{\small SQOPT}} \providecommand{\IOTR }{{\small IOTR}} \providecommand{\APPSPACK}{{\small APPSPACK}} \providecommand{\CGM }{{\small CGM}} \providecommand{\GMRES }{{\small GMRES}} \providecommand{\LSQR }{{\small LSQR}} \providecommand{\MINRES}{{\small MINRES}} \providecommand{\SYMMLQ}{{\small SYMMLQ}} \providecommand{\LRHR}{{\small L-RHR}} \makeatother %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: