# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/f(x)inF;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.gif"
 ALT="$f(x)\in F$">|; 

$key = q/y^1,...,y^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.gif"
 ALT="$y^1,...,y^n$">|; 

$key = q/displaystyleR(x)={{bf{E}f(x)=int_Ff(x)dP(f(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.gif"
 ALT="$\displaystyle R(x) = {\bf E} f(x) = \int_F f(x) dP(f(x)$">|; 

$key = q/http:slashslashpilis.if.ktu.ltslashtilde{}jmockus;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.gif"
 ALT="$http://pilis.if.ktu.lt/\tilde{} jmockus$">|; 

$key = q/x_2ge0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.gif"
 ALT="$x_2 \ge 0$">|; 

$key = q/l=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.gif"
 ALT="$l=0$">|; 

$key = q/F;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.gif"
 ALT="$F$">|; 

$key = q/f(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.gif"
 ALT="$f(x)$">|; 

$key = q/a_jlex_j^ileb_j,j=1,...,m,i=1,...,n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.gif"
 ALT="$a_j \le x_j^i \le b_j, j=1,...,m, i=1,...,n$">|; 

$key = q/phi^n,omega^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.gif"
 ALT="$\phi^n,\omega^n$">|; 

$key = q/y^n=f(x^n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.gif"
 ALT="$y^n=f(x^n)$">|; 

$key = q/textstyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.gif"
 ALT="$\textstyle =$">|; 

$key = q/r_i^l=h_i^lslashsum_jh_j^l,l=0,1,infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.gif"
 ALT="$r_i^l=h_i^l / \sum_j h_j^l, l=0,1,\infty $">|; 

$key = q/R_0(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.gif"
 ALT="$R_0(x)$">|; 

$key = q/h_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.gif"
 ALT="$h_j$">|; 

$key = q/phi(omega),omegainR^{m_o};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.gif"
 ALT="$\phi(\omega),\omega \in R^{m_o}$">|; 

$key = q/omega^n(h);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.gif"
 ALT="$\omega^n(h)$">|; 

$key = q/epsfig{figure=video-wiener-col.eps,width=linewidth};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="422" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img91.gif"
 ALT="\epsfig{figure=video-wiener-col.eps,width=\linewidth}">|; 

$key = q/phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.gif"
 ALT="$\phi$">|; 

$key = q/h_i=max_jh_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.gif"
 ALT="$h_i=\max_j h_j$">|; 

$key = q/epsfig{figure=school-stud.eps,width=linewidth};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="34" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img87.gif"
 ALT="\epsfig{figure=school-stud.eps,width=\linewidth}">|; 

$key = q/x=(x_0,x_1,x_{infty});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.gif"
 ALT="$x=(x_0, x_1, x_{\infty})$">|; 

$key = q/epsfig{figure=pack-color2better.eps,width=12.0cm};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="544" HEIGHT="410" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img67.gif"
 ALT="\epsfig{figure=pack-color2better.eps,width=12.0cm}">|; 

$key = q/displaystylecases{e^{{-h_{i+1}overx_2slashln(1+N)}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img76.gif"
 ALT="$\displaystyle \cases {e^{{-h_{i+1} \over x_2 /\ln (1+N)}},$">|; 

$key = q/h=h(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.gif"
 ALT="$h=h(x)$">|; 

$key = q/displaystylex^{n+1}=argmin_{1leilen}f(x^i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.gif"
 ALT="$\displaystyle x^{n+1}= arg \min_{1 \le i \le n} f(x^i)$">|; 

$key = q/nu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img42.gif"
 ALT="$\nu$">|; 

$key = q/http:slashslashproin.ktu.ltslashtilde{}mockus;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="422" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.gif"
 ALT="$http://proin.ktu.lt/\tilde{}mockus$">|; 

$key = q/phi(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.gif"
 ALT="$\phi(\omega)$">|; 

$key = q/r_j=rho_x(h_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.gif"
 ALT="$r_j=\rho_x(h_j)$">|; 

$key = q/f_K(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.gif"
 ALT="$f_K(x)$">|; 

$key = q/l=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img59.gif"
 ALT="$l=1$">|; 

$key = q/rho_x(h_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.gif"
 ALT="$\rho_x(h_j)$">|; 

$key = q/f(x),xinR^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.gif"
 ALT="$f(x), x \in R^m$">|; 

$key = q/i+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.gif"
 ALT="$i+1$">|; 

$key = q/x^n=(x_1^n,....,x_m^n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.gif"
 ALT="$x^n=(x_1^n,....,x_m^n)$">|; 

$key = q/y^0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.gif"
 ALT="$y^0$">|; 

$key = q/f(x)<y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.gif"
 ALT="$f(x)&lt;y$">|; 

$key = q/x_3ge0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="549" HEIGHT="659" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.gif"
 ALT="$x_3 \ge 0$">|; 

$key = q/R_0(x)={{bf{E}f(x)-{{bf{E}f(x^*);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.gif"
 ALT="$R_0(x)={\bf E} f(x) - {\bf E} f(x^*)$">|; 

$key = q/r(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.gif"
 ALT="$r(x)$">|; 

$key = q/f(x)=f(x,nu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.gif"
 ALT="$f(x)=f(x,\nu)$">|; 

$key = q/F^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img25.gif"
 ALT="$F^n$">|; 

$key = q/displaystylecases{e^{{-h_{i+1}overx_2slashln(1+x_3N)}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img82.gif"
 ALT="$\displaystyle \cases {e^{{-h_{i+1} \over x_2 /\ln (1+x_3 N)}},$">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img77.gif"
 ALT="$N$">|; 

$key = q/y_i=f(x_i),i=1,...,n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.gif"
 ALT="$y_i=f(x_i), i=1,...,n$">|; 

$key = q/x_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.gif"
 ALT="$x_2$">|; 

$key = q/r_i^{infty}=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.gif"
 ALT="$r_i^{\infty}=1$">|; 

$key = q/omega^n=omega^n(h);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.gif"
 ALT="$\omega^n=\omega^n(h)$">|; 

$key = q/epsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img92.gif"
 ALT="$\epsilon$">|; 

$key = q/r(x)=f(x)-f(x^*);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.gif"
 ALT="$r(x)=f(x)-f(x^*)$">|; 

$key = q/s_n(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.gif"
 ALT="$s_n(x)$">|; 

$key = q/P;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.gif"
 ALT="$P$">|; 

$key = q/f(x)=phi(omega^n(h(x)));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.gif"
 ALT="$f(x)=\phi(\omega^n(h(x)))$">|; 

$key = q/epsfig{figure=gmj-bayes-projx-col.eps,width=linewidth};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="556" HEIGHT="422" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.gif"
 ALT="\epsfig{figure=gmj-bayes-projx-col.eps,width=\linewidth}">|; 

$key = q/phi^n=phi(omega^n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.gif"
 ALT="$\phi^n=\phi(\omega^n)$">|; 

$key = q/y^i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.gif"
 ALT="$y^i$">|; 

$key = q/x^*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.gif"
 ALT="$x^*$">|; 

$key = q/h_j=c_jslashg_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.gif"
 ALT="$h_j=c_j/g_j$">|; 

$key = q/x_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.gif"
 ALT="$x_3$">|; 

$key = q/h_i=v(y^i)-v(y^0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.gif"
 ALT="$h_i=v(y^i)-v(y^0)$">|; 

$key = q/displaystyleP^n(y,x)=P(f(x)<y|f(x^i)<y^i,i=1,...,n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.gif"
 ALT="$\displaystyle P^n(y,x)=P(f(x)&lt;y\vert f(x^i)&lt; y^i, i=1,...,n)$">|; 

$key = q/K;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.gif"
 ALT="$K$">|; 

$key = q/x=(x_1,x_2,x_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="352" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.gif"
 ALT="$x=(x_1,x_2,x_3)$">|; 

$key = q/P(f(x)<y|f(x^i)<y^i,i=1,...,n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.gif"
 ALT="$P(f(x)&lt;y\vert f(x^i)&lt; y^i, i=1,...,n)$">|; 

$key = q/(y^n,x^n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.gif"
 ALT="$(y^n,x^n)$">|; 

$key = q/displaystyler_{i+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.gif"
 ALT="$\displaystyle r_{i+1}$">|; 

$key = q/ln(1+N);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="14" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.gif"
 ALT="$\ln
(1+N)$">|; 

$key = q/x=(x_1,...,x_m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.gif"
 ALT="$x=(x_1,...,x_m)$">|; 

$key = q/http:slashslasheta.ktl.mii.ltslashtilde{}mockus;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.gif"
 ALT="$http://eta.ktl.mii.lt/\tilde{}mockus$">|; 

$key = q/epsfig{figure=gmj-exkor-projx-col.eps,width=linewidth};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="556" HEIGHT="419" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img47.gif"
 ALT="\epsfig{figure=gmj-exkor-projx-col.eps,width=\linewidth}">|; 

$key = q/x_j^i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.gif"
 ALT="$x_j^i$">|; 

$key = q/R(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.gif"
 ALT="$R(x)$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.gif"
 ALT="$i$">|; 

$key = q/phi(omega)inPhi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.gif"
 ALT="$\phi(\omega) \in \Phi$">|; 

$key = q/xinR^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.gif"
 ALT="$x\in R^m$">|; 

$key = q/epsfig{figure=gmj-cut-out-pattern-col.eps,width=12.0cm};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="414" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img66.gif"
 ALT="\epsfig{figure=gmj-cut-out-pattern-col.eps,width=12.0cm}">|; 

$key = q/r_i^{infty}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.gif"
 ALT="$r_i^{\infty}= 0$">|; 

$key = q/epsilon-bounds;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.gif"
 ALT="$\epsilon-bounds$">|; 

$key = q/P^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.gif"
 ALT="$P^n$">|; 

$key = q/epsfig{figure=shed-out.eps,width=linewidth};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="34" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img86.gif"
 ALT="\epsfig{figure=shed-out.eps,width=\linewidth}">|; 

$key = q/x_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.gif"
 ALT="$x_1$">|; 

$key = q/http:slashslashmockus.usslashoptimum;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.gif"
 ALT="$http://mockus.us/optimum$">|; 

$key = q/infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img60.gif"
 ALT="$\infty$">|; 

$key = q/Phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.gif"
 ALT="$\Phi$">|; 

$key = q/N=K;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img80.gif"
 ALT="$N=K$">|; 

$key = q/h;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.gif"
 ALT="$h$">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.gif"
 ALT="$x$">|; 

$key = q/n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.gif"
 ALT="$n$">|; 

$key = q/{{bf{E}f(x^*);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.gif"
 ALT="${\bf E} f(x^*)$">|; 

$key = q/l=0,1,infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.gif"
 ALT="$l=0,1,\infty$">|; 

$key = q/j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.gif"
 ALT="$j$">|; 

1;

