function ncqptraj

%
%                    min -2(x-0.25)^2 + 2(y-0.5)^2
%                          st   x+ y <= 1
%                               3x+y <= 1.5
%                              (x,y) >= 0
%
% 22/Jun/99
%

clear

h_space = 0.001;
%h_space = 0.05;
v_space = 0.2;
c_space = 1.0;

[X,Y]=meshgrid(-0.1:h_space:0.6,-0.1:h_space:0.6) ;
[f,fc1,fc2,fc3,fc4,fint] = pf( X , Y ) ;

colormap gray

contourf(X,Y,-fc1,[0 0], 'k' );

hold on

contourf(X,Y,-fc2,[0 0], 'k' );
contourf(X,Y,-fc3,[0 0], 'k' );
contourf(X,Y,-fc4,[0 0], 'k' );

colormap flag

%colormap cool
colormap summer

%colormap('default')

nz = -15:v_space:30 ;
nz2 = -15:c_space:2 ;
contour(X,Y,f,nz,'y');
%contour(X,Y,f,nz,'g');
%[C,h] = contour(X,Y,f,nz,'y');
%clabel(C,nz2)

hold on

contour(X,Y,fint,nz,'g');

contour(X,Y,-fc1,[0 0], 'k' );
contour(X,Y,-fc2,[0 0], 'k' );
contour(X,Y,fc3,[0 0], 'k' );
contour(X,Y,fc4,[0 0], 'k' );

u1 = [ ...
  1.63301930720532E-01 ...
  1.63301930605655E-01 ...
  1.63301930546201E-01 ...
  1.63301930485363E-01 ...
  1.63301930423108E-01 ...
  1.63301930359402E-01 ...
  1.63301930294213E-01 ...
  1.63301930227505E-01 ...
  1.63301930159243E-01 ...
  1.63301930089392E-01 ...
  1.63301930017913E-01 ...
  1.63301929944769E-01 ...
  1.63301929869922E-01 ...
  1.63301929793331E-01 ...
  1.63301929714956E-01 ...
  1.63301929634756E-01 ...
  1.63301929552687E-01 ...
  1.63301929468707E-01 ...
  1.63301929382770E-01 ...
  1.63301929294832E-01 ...
  1.63301929204846E-01 ...
  1.63301929112764E-01 ...
  1.63301929018536E-01 ...
  1.63301928922114E-01 ...
  1.63301928823446E-01 ...
  1.63301928722479E-01 ...
  1.63301928619161E-01 ...
  1.63301928513436E-01 ...
  1.63301928405249E-01 ...
  1.63301928294542E-01 ...
  1.63301928181255E-01 ...
  1.63301928065330E-01 ...
  1.63301927946705E-01 ...
  1.63301927825317E-01 ...
  1.63301927701101E-01 ...
  1.63301927573992E-01 ...
  1.63301927443922E-01 ...
  1.63301927310822E-01 ...
  1.63301927174622E-01 ...
  1.63301927035250E-01 ...
  1.63301926892631E-01 ...
  1.63301926746690E-01 ...
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  1.63301926444531E-01 ...
  1.63301926288153E-01 ...
  1.63301926128132E-01 ...
  1.63301925964384E-01 ...
  1.63301925796821E-01 ...
  1.63301925625356E-01 ...
  1.63301925449896E-01 ...
  1.63301925270350E-01 ...
  1.63301925086621E-01 ...
  1.63301924898613E-01 ...
  1.63301924706225E-01 ...
  1.63301924509356E-01 ...
  1.63301924307902E-01 ...
  1.63301924101755E-01 ...
  1.63301923890806E-01 ...
  1.63301923674944E-01 ...
  1.63301923454054E-01 ...
  1.63301923228018E-01 ...
  1.63301922996717E-01 ...
  1.63301922760029E-01 ...
  1.63301922517827E-01 ...
  1.63301922269984E-01 ...
  1.63301922016368E-01 ...
  1.63301921756845E-01 ...
  1.63301921491276E-01 ...
  1.63301921219521E-01 ...
  1.63301920941437E-01 ...
  1.63301920656875E-01 ...
  1.63301920365685E-01 ...
  1.63301920067712E-01 ...
  1.63301919762798E-01 ...
  1.63301919450782E-01 ...
  1.63301919131498E-01 ...
  1.63301918804777E-01 ...
  1.63301918470446E-01 ...
  1.63301918128328E-01 ...
  1.63301917778240E-01 ...
  1.63301917419998E-01 ...
  1.63301917053411E-01 ...
  1.63301916678285E-01 ...
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  1.63301915901617E-01 ...
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  1.63301915088345E-01 ...
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  1.63301913796011E-01 ...
  1.63301913345011E-01 ...
  1.63301912883505E-01 ...
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  1.63301911927995E-01 ...
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  1.63301909337534E-01 ...
  1.63301908782682E-01 ...
  1.63301908214906E-01 ...
  1.63301907633906E-01 ...
  1.63301907039371E-01 ...
  1.63301906430989E-01 ...
  1.63301905808435E-01 ...
  1.63301905171380E-01 ...
  1.63301904519487E-01 ...
  1.63301903852408E-01 ...
  1.63301903169792E-01 ...
  1.63301902471275E-01 ...
  1.63301901756488E-01 ...
  1.63301901025051E-01 ...
  1.63301900276577E-01 ...
  1.63301899510669E-01 ...
  1.63301898726920E-01 ...
  1.63301897924916E-01 ...
  1.63301897104231E-01 ...
  1.63301896264429E-01 ...
  1.63301895405066E-01 ...
  1.63301894525685E-01 ...
  1.63301893625822E-01 ...
  1.63301892704997E-01 ...
  1.63301891762724E-01 ...
  1.63301890798503E-01 ...
  1.63301889811822E-01 ...
  1.63301888802159E-01 ...
  1.63301887768977E-01 ...
  1.63301886711729E-01 ...
  1.63301885629855E-01 ...
  1.63301884522781E-01 ...
  1.63301883389920E-01 ...
  1.63301882230671E-01 ...
  1.63301881044420E-01 ...
  1.63301879830537E-01 ...
  1.63301878588380E-01 ...
  1.63301877317289E-01 ...
  1.63301876016590E-01 ...
  1.63301874685594E-01 ...
  1.63301873323596E-01 ...
  1.63301871929872E-01 ...
  1.63301870503685E-01 ...
  1.63301869044277E-01 ...
  1.63301867550875E-01 ...
  1.63301866022688E-01 ...
  1.63301864458904E-01 ...
  1.63301862858696E-01 ...
  1.63301861221213E-01 ...
  1.63301859545589E-01 ...
  1.63301857830935E-01 ...
  1.63301856076341E-01 ...
  1.63301854280877E-01 ...
  1.63301852443592E-01 ...
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  1.63301836117931E-01 ...
  1.63301833857576E-01 ...
  1.63301831544572E-01 ...
  1.63301829177691E-01 ...
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  1.63301821741090E-01 ...
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  1.63301813772629E-01 ...
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  1.63301808146169E-01 ...
  1.63301805234270E-01 ...
  1.63301802254543E-01 ...
  1.63301799205410E-01 ...
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  1.63301789625215E-01 ...
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  1.63301779359852E-01 ...
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  1.63301768360318E-01 ...
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  1.63301640101782E-01 ...
  1.63301633275633E-01 ...
  1.63301626290483E-01 ...
  1.63301619142629E-01 ...
  1.63301611828279E-01 ...
  1.63301604343558E-01 ...
  1.63301596684495E-01 ...
  1.63301588847030E-01 ...
  1.63301580827008E-01 ...
  1.63301572620176E-01 ...
  1.63301564222183E-01 ...
  1.63301555628576E-01 ...
  1.63301546834799E-01 ...
  1.63301537836189E-01 ...
  1.63301528627976E-01 ...
  1.63301519205276E-01 ...
  1.63301509563094E-01 ...
  1.63301499696318E-01 ...
  1.63301489599716E-01 ...
  1.63301479267935E-01 ...
  1.63301468695497E-01 ...
  1.63301457876795E-01 ...
  1.63301446806095E-01 ...
  1.63301435477527E-01 ...
  1.63301423885083E-01 ...
  1.63301412022618E-01 ...
  1.63301399883842E-01 ...
  1.63301387462318E-01 ...
  1.63301374751462E-01 ...
  1.63301361744533E-01 ...
  1.63301348434635E-01 ...
  1.63301334814711E-01 ...
  1.63301320877540E-01 ...
  1.63301306615733E-01 ...
  1.63301292021727E-01 ...
  1.63301277087785E-01 ...
  1.63301261805989E-01 ...
  1.63301246168236E-01 ...
  1.63301230166235E-01 ...
  1.63301213791502E-01 ...
  1.63301197035355E-01 ...
  1.63301179888910E-01 ...
  1.63301162343075E-01 ...
  1.63301144388548E-01 ...
  1.63301126015809E-01 ...
  1.63301107215116E-01 ...
  1.63301087976503E-01 ...
  1.63301068289768E-01 ...
  1.63301048144474E-01 ...
  1.63301027529938E-01 ...
  1.63301006435233E-01 ...
  1.63300984849172E-01 ...
  1.63300962760312E-01 ...
  1.63300940156940E-01 ...
  1.63300917027073E-01 ...
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  1.63300869138512E-01 ...
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  1.63300793040943E-01 ...
  1.63300766484335E-01 ...
  1.63300739309151E-01 ...
  1.63300711500983E-01 ...
  1.63300683045085E-01 ...
  1.63300653926372E-01 ...
  1.63300624129404E-01 ] ;

u2 = [ ...
  1.63300593638384E-01 ...
  1.63300562437144E-01 ...
  1.63300530509143E-01 ...
  1.63300497837453E-01 ...
  1.63300464404750E-01 ...
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  1.63300167330425E-01 ...
  1.63300126199332E-01 ...
  1.63300084110188E-01 ...
  1.63300041040677E-01 ...
  1.63299996967965E-01 ...
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  1.63299905718924E-01 ...
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  1.63299810169525E-01 ...
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  1.63299710117104E-01 ...
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  1.63299605349450E-01 ...
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  1.63299198226153E-01 ...
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  1.63140997120021E-01 ...
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v8 = [ ...
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v = [ v1 v2 v3 v4 v5 v6 v7 v8 ] ;
plot(u,v,'r', 'LineWidth',2)

axis off

s = [ 0.0E-01 ] ;
t = [ 5.0E-01 ] ;

plot( s, t, 'ro', 'MarkerEdgeColor','k', 'MarkerFaceColor','r', 'MarkerSize',4)

s = [ 1.63301937639297E-01 ] ;
t = [ 3.03755212285449E-01 ] ;

plot( s, t, 'bo', 'MarkerEdgeColor','k', 'MarkerFaceColor','b', 'MarkerSize',4)

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  4.68750000922376E-01 ] ;

s = [ 3.03177230650158E-01 ] ;
t = [   4.78366194152536E-01 ] ;

plot( s, t, 'ro', 'MarkerEdgeColor','k', 'MarkerFaceColor','m', 'MarkerSize',4)

plot(q,r,'r', 'LineWidth',2)

s = [ 3.43749992176856E-01 ] ;
t = [ 4.68750000922376E-01 ] ;

plot( s, t, 'ro', 'MarkerEdgeColor','k', 'MarkerFaceColor','r', 'MarkerSize',4)

hold off

print -depsc eps/ncqptraj

% penalty function

function [f,fc1,fc2,fc3,fc4,fint] = pf( x, y )
rho = 1000000000000000.0 ;
f = obj( x, y ) ;
fc1= - c1( x, y ) ;
fc2= - c2( x, y ) ;
fc3= c3( x, y ) ;
fc4= c4( x, y ) ;
fint = f-rho*(min(fc1,0)+min(fc2,0)+min(fc3,0)+min(fc4,0)) ;

function o = obj( x, y )
o = -2*(x-0.25).^2 + 2*(y-0.5).^2 ;

function c = c1( x, y )
c = x + y - 1;

function c = c2( x, y )
c = 3 * x + y - 1.5 ;

function c = c3( x, y )
c = x ;

function c = c4( x, y )
c = y ;






