# is it possible to combine a step monitor with a 3d contour plot

ph = 80;
pc = 20;
kp = 0.5;
kc = 0.5;
kh = 0.778;
rt = 0.25;
rd = 0.1;
td = 10;
cfc = 10;
cfh = 10;
cobr0 = 68000;
ios0 = 75488.9;

c = {(120 - t1)*cfh == (t2 - 70)*cfc,
fic == (t1 - 60)*cfh,
fih == (140 - t2) + cfc,
cobr == (pc*fic) + (ph*fih),
ap == (cfh*(120 - t1))/(kp*(120 - t2)),
ac == fic/(kc*dtc),
ah == fih/(kh*dth),
dtp == (((120 - t2)*(t1 - 70)*(((120 - t2) + (t1 - 70))/2)))^(1/3),
dtc == (((t1 - 35)*40*(((t1 - 35) + 40)/2)))^(1/3),
dth == ((40*(179 - t2)*((40 + 179 - t2)/2)))^(1/3), t1 >= 80,
t2 <= 110, dtp > 30, dtc > 30, dth > 30, ap >= 0, ah >= 0, ac >= 0};

ios = 6110*((ap + 0.00000001)^0.65 + (ac + 0.000000001)^0.65 + (ah +
0.000000001)^0.65);

pts = NMinimize[{ios, c}, {ap, ac, ah, dtc, dth, dtp, cobr, fih, fic,
StepMonitor :> (Sow[{ac, ah, ap}])] // Reap;

ContourPlot3D[ios, {ac, 0, 2}, {ah, 0, 2}, {ap, 0, 2},
Contours -> 10,
Epilog -> ({Red, PointSize[0.01], Line[pts[[2, 1]]], Yellow,
Point /@ pts[[2, 1]], Blue, PointSize[0.02],
Point[pts[[2, 1, 1]]]})]


So here is my problem. I can get the global optimum and i can create a 3d contour plot, but i can't figure out how to combine a step monitor with all of the above (or if it's even possible)

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Show[ContourPlot3D[ios, {ac, 0, 2}, {ah, 0, 2}, {ap, 0, 2}, Contours -> 10], Graphics3D@({Red, PointSize[0.01], Line[pts[[2, 1]]], Yellow, Point /@ pts[[2, 1]], Blue, PointSize[0.02], Point[pts[[2, 1, 1]]]})] – Dr. belisarius Jan 30 '14 at 19:38
This seems to do the trick. Thank you very much. – user 3 50 Jan 30 '14 at 19:54

Only for this question not getting to the un-answered queue:

Show[ContourPlot3D[ios, {ac, 0, 2}, {ah, 0, 2}, {ap, 0, 2}, Contours -> 10],
Graphics3D@({Red, PointSize[0.01], Line[pts[[2, 1]]], Yellow, Point /@ pts[[2, 1]],
Blue, PointSize[0.02], Point[pts[[2, 1, 1]]]})]

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i'm sorry i am a bit new here so i didn't know the protocol. – user 3 50 Jan 30 '14 at 20:17
@user12073 You haven't done anything wrong. Welcome to the site. When you have doubts about the site etiquette you can ask in chat chat.stackexchange.com/rooms/2234/wolfram-mathematica – Dr. belisarius Jan 30 '14 at 20:23