## 28 Reputation

16 years, 355 days

## maybe not in that case?...

Hi, I have no time to prove the identity you mentioned here, but even if it were true, it might not work in the case as the matrix K is a singular one. I am eager to see the proof first of all.

Removed.

## I like the solution, but it would be dif...

I like the solution that Roman posted but I must admit it would be rather difficult for me to think of. Thereby, I paste my rather heuristic one: ```Obj := (1/4*a+3/4*a+7/8*a+a+15/8*a+2*a +19/8*a+21/8*a-1/4*b-3/4*b-7/8*b-b-15/8*b -2*b-19/8*b-21/8*b)^2+(1/4*b+3/4*b+7/8*b+b +15/8*b+2*b+19/8*b+21/8*b-1/4*a-3/4*a-7/8*a -a-15/8*a-2*a-19/8*a-21/8*a)^2;``` ```#noting symetry, lets incorporate variable c=a-b into the model rep:={seq(a[i]=c[i]+b[i],i=1..8)}: New_obj:=subs(rep,Obj);``` ```#as New_obj satisfies the equation #New_Obj = 2*(nObj)^2 implying thus that #maximum of New_Obj and nObj considering resp. constraints #are accomplished whenever nObj is max or min #we need only to adjust constraints for c #de facto it is sufficient to find maximum of nObj only #and taking -1*nObj yelds min nObj:=1/4*c+3/4*c+7/8*c+c+15/8*c+2*c+19/8*c+21/8*c; nC1:=add(c[i],i=1..8)=0; nC2:=seq(c[i]^2=1,i=1..8); with(Optimization): NLPSolve(nObj, {nC1, nC2}, maximize=true): extremum_of_nObj:=%; ext_at_point=%%; clearly New_Obj is nonnegative and the question is if it can be zero 'solve' provides the answer here_nObj_is_zero=solve({nObj, nC1, nC2}, {seq(c[i],i=1..8)}); ```

## This is weird!...

Maybe I'm missing something, but it appears to me as: Obj:=(1/4*a+3/4*a+7/8*a+15/8*a+2*a+19/8*a+21/8*a+1/4*b+ 3/4*b+7/8*b+15/8*b+2*b+19/8*b+21/8*b)^2= 1/4*(a+b)+3/4*(a+b)+7/8*(a+b)+...+21/8*(a+b) what in connection with CON3 is equal to 1/4+3/4+7/8+...+21/8, which is constant and there is nothing to minimize! What is it about, then?

## For me its a LP...

As I noticed, the obj. function is a square of a linear combination of a's and b's.

## making [a=1, b=2, c=3, and so on]...

Why did none of you mention the 'Equate' command?? it solves the first problem offhand, doesn't it? Happy New Year....
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