A possible typo in the program of "Mathematica Navigator" by Heikki

• To: mathgroup at smc.vnet.net
• Subject: [mg122114] A possible typo in the program of "Mathematica Navigator" by Heikki
• From: Nabeel Butt <nabeel.butt at gmail.com>
• Date: Sat, 15 Oct 2011 06:02:16 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Dear All,
In the chapter on 'optimization' the book presents a program to
implement Kuhn Tucker conditions.I have indicated where the book appears to
make the typo in the code I show below :

kktOptimize[f_, g_List, h_List, x_List, \[Epsilon]_: 10.^-12] :=
Module[{\[Lambda]\[Lambda] =
Array[\[Lambda], Length[g]], \[Mu]\[Mu] = Array[\[Mu], Length[h]],
x\[Lambda]\[Mu], eqns, sol, realsol, nrealsol, ineqs, pos, cand},
x\[Lambda]\[Mu] = Join[x, \[Lambda]\[Lambda], \[Mu]\[Mu]];
Join[D[f + \[Lambda]\[Lambda].g + \[Mu]\[Mu].h, {x}],
g, \[Mu]\[Mu] h] == 0];

sol = Union[Solve[eqns, x\[Lambda]\[Mu]]];

realsol = Select[sol, FreeQ[Chop[N[#], \[Epsilon]], Complex] &];
If[realsol == {},
Return["No real solutions; try a larger \[Epsilon]"]];
nrealsol =
Chop[N[x\[Lambda]\[Mu] /. realsol], \[Epsilon]];

(*Here below this line the book makes a typo and I have made the appropriate
correction -instead of  just h<=epsilon it also joined the mu vector *)

pos = Position[(And @@ #) & /@ (ineqs /. nrealsol), True];
If[pos == {},
Return["Inequalities not satisfied; try a larger \[Epsilon]"]];
cand = Union[Sort /@ Extract[realsol, pos]];
First[Sort[Transpose[{f /. cand, cand}], #1[[1]] < #2[[1]] &]]]

Now the above program works fine after I have made the correction.For
example you can run :
f = -((x - 2)^(1.5) + (y - 3)^2);
h1 = x + y - 9;
h2 = 2 - x;
h3 = 3 - y;
kktOptimize[f, {}, {h1, h2, h3}, {x, y}]

OR if you are too eager :
f = -((Log /@ x - 2)^(1.5) + (y - 3)^2);
h1 = x + y - 9;
h2 = 2 - x;
h3 = 3 - y;
kktOptimize[f, {}, {h1, h2, h3}, {x, y}]

Work fines now.Perhaps you guys already know but it is good to point out
errors so that they could be corrected in the next edition !.
It is also possible I am wrong so nice to know if I am making errors !
Thanks...
Nabeel

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Nabeel Butt
UWO,London