i need to find the optimize values of R for a values in an interval but R values are in form of the root of the equation; how to solve this sir? for simple equation it was ok.

Question

arpan garg 2022-7-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1771215-i-need-to-find-the-optimize-values-of-r-for-a-values-in-an-interval-but-r-values-are-in-form-of-the

评论： arpan garg 2022-8-4

syms R a
%t=solve(100*a^16-R^8==0,R)
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==0,R)
%a=(.1:.001:5);
a1=1;a2=5;
for i=1:1:8         %because t is representing 8 different R roots of given equation.
    n=matlabFunction(t(i,1))
    m=fminbnd(n,a1,a2)     % finding minimum of every R value
end

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Answer 1

Torsten 2022-7-30

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1771215-i-need-to-find-the-optimize-values-of-r-for-a-values-in-an-interval-but-r-values-are-in-form-of-the#answer_1018340

编辑：Torsten 2022-7-30

在 MATLAB Online 中打开

I think this is the safest way:

syms R a

p = 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;

alow = 1.0;

ahigh = 10.0;

A = alow:0.01:ahigh;

minimum = Inf;

I = 0;

for i = 1:numel(A)

aa = A(i);

pp = subs(p,a,aa);

pp_num = sym2poly(pp);

r = roots(pp_num);

r = r(abs(imag(r)) < 1e-10);

rmin = min(real(r));

RR(i) = rmin;

if rmin < minimum

minimum = rmin;

I = i;

end

minimum

minimum = 5.8174e+03

A(I)

ans = 4.5100

plot(A,RR)

5 个评论
显示 3更早的评论隐藏 3更早的评论

arpan garg 2022-8-4

sorry to bother you again sir but i if change my p value then it is showing some error.

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Torsten 2022-8-4

Maybe of help:

https://de.mathworks.com/matlabcentral/answers/141712-error-in-expand-bigprod-integer-too-large-in-context

arpan garg 2022-8-4

Thanks Torsten,

finally I have to leave this code.

请先登录，再进行评论。

Answer 2

Torsten 2022-7-30

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1771215-i-need-to-find-the-optimize-values-of-r-for-a-values-in-an-interval-but-r-values-are-in-form-of-the#answer_1018255

编辑：Torsten 2022-7-30

在 MATLAB Online 中打开

Try "fmincon" for the problem

min: R
s.c.
f(R,a) = 0  (f is the complete expression between "t=solve(" and "==0,R))
a_left <= a <= a_right

f can be prescribed in function "nonlcon".

The unknowns are R and a.

So no need to solve directly for R as a function of a.

5 个评论
显示 3更早的评论隐藏 3更早的评论

Torsten 2022-7-30

编辑：Torsten 2022-7-30

在 MATLAB Online 中打开

x0 = [3,3];
lb = [-Inf,1];
ub = [Inf,5];
obj = @(x) x(1);
sol = fmincon(obj,x0,[],[],[],[],lb,ub,@nonlcon);
Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.
R = sol(1)
R = 5.8174e+03
a = sol(2)
a = 4.5130
[~, ceq] = nonlcon(sol)
ceq = -1.9828e-118
function [c,ceq] = nonlcon(x)
  R = x(1);
  a = x(2);
  c = [];
  ceq = 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;
end

Octave gives:

R = -4.6875e+04

a = 1

Torsten 2022-7-30

编辑：Torsten 2022-7-30

在 MATLAB Online 中打开

Also, the verified outcome are R=5888.547380 at a=4.44580555360928.

But R = 5817.4 at a = 4.5130 is lower ...

Save

function [c,ceq] = nonlcon(x)
  R = x(1);
  a = x(2);
  c = [];
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;
end

as nonlcon.m and only run the script

x0 = [3,3];
lb = [-Inf,1];
ub = [Inf,5];
obj = @(x) x(1);
sol = fmincon(obj,x0,[],[],[],[],lb,ub,@nonlcon);

from the MATLAB editor. This should work in R2015.

Or don't you have a licence for the optimization toolbox ?

The way with fminbnd will not work since there is no explicit formula for the roots of polynomials of degree >4 (except for trivial cases as e.g. your test equation 100*a^16-R^8==0). Or is your solve-command with the nasty function successful ?

arpan garg 2022-7-30

sorry R value is 5488.547380 at a=4.44580555360928.

Torsten 2022-7-30

编辑：Torsten 2022-7-30

在 MATLAB Online 中打开

sorry R value is 5488.547380 at a=4.44580555360928

Doesn't seem to be correct: R = 5819.0523324 at a = 4.44580555360928.

Maybe there is an error in your "long formula" or there is a problem with the precision of the root calculation.

Yes, the latter will be the case. It's impossible to get reliable roots because the polynomial coefficients in R are of the order 1e-101 !!!!

syms R a
p = 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;
aa = 4.44580555360928;
pp = subs(p,a,aa);
format long
r = double(vpa(root(pp,R)))
r = 8×1
1.0e+08 *

   0.000058190523324
   0.000478658482639
   0.002251774276746
   0.007714554876288
   0.023378065058889
   0.060794677502264
   0.444665139925285
   1.232925568902310
pp_num = sym2poly(pp).'
pp_num = 9×1
1.0e-101 *

   0.000000000000000
  -0.000000000000000
   0.000000000000000
  -0.000000000000000
   0.000000000000000
  -0.000000000000023
   0.000000004429345
  -0.000182756171386
   0.917906651329423
roots(pp_num)
ans = 8×1
1.0e+08 *

   1.232925568902309
   0.444665139925284
   0.060794677502264
   0.023378065058889
   0.007714554876288
   0.002251774276746
   0.000478658482639
   0.000058190523324