@Markiyan Hirnyk  Replace  x+y+z = 2  by  x+y+z = 1  as this is in  OP  task.

Addition: Certainly, at some  values of parameters the minimum may not be achieved (unbounded problem)

@mangaba  I have no problem in Maple 2015 (32 bit) on Windows 8.1

@Shervin  zip  command implements elementwise union of two lists into a single list according to the specified rule.  *~ binary operation  (in  tomleslie's answer) makes the same, but it works in the later versions Maple only.

Alejandro Jakubi  and  Preben Alsholm . Thank you very much for your interest and the analysis carried out.

@Axel Vogt  but still would like to know the cause of the error.

@Rouben Rostamian   Agreed that the basis for my solution is your idea. But it has been improved: now user can explicitly specify a range for the variable  w . 

@Markiyan Hirnyk  You are absolutely right, so vote up from me.

@Carl Love  Thank you for your helpful comment.

@Carl Love  Thank you for the quick response and solution to the problem. 

@acer  I figured it out just like you, but maybe OP just confuses these interfaces.

@mapleatha  Acer's method and old reference worked for me also (only in  Standard worksheet rather than Classic worksheet).

@Carl Love   Thank you for the detection of serious gap in my decision.

@nMaple  Select  remember table assignment  and press  OK

@Markiyan Hirnyk  For  n=4  Maple 2015 works incorrectly. Here is the calculation in Maple 16 with visualization:

restart;

P := combinat[choose]({$1 .. 4}, 2):

S := combinat[powerset](P):

L := [seq(GraphTheory[Graph](4, S[k]), k = 1 .. nops(S))]:

M := [ListTools[Categorize]((x, y)-> GraphTheory[IsIsomorphic](x, y), L)]:

K := [seq(M[i, 1], i = 1 .. nops(M))]:

nops(K);

plots[display](Matrix(3, 5, [seq(GraphTheory[DrawGraph](K[k]), k = 1 .. 11), plot([[0, 0]], axes = none)$4]), scaling = constrained);

@Markiyan Hirnyk   

See   http://oeis.org/search?q=1%2C1%2C2%2C4%2C11%2C34&sort=&language=english&go=Search