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Hi

I am trying to solve the following set of equations but the solver is prematurely stopped and If I alter the MaxIter and MaxEvals then also its showing stopped prematurelly and then I tried to alter the tolerance then its shows no solution found. Can anyone guide how can i obtain the solution for the following set of equations.

function F = compare(X)

rho=1000.0;

F=[

1.0*7.018e-4*4.2850022315+-1.0*1.25e-3*X(2)+-1.0*7.36e-5*X(3)+-1.0*4.47e-5*(4);

-1.0*1.25e-3*X(1)+1.0*1.66e-5*X(4)+1.0*4.47e-5*X(5)+1.0*1.07e-4*X(6);

+1.0*7.36e-5*X(2)-1.0*1.07e-4*X(6)+1.0*1.07e-4*X(7);

1.0*4.47e-5*X(3)+-1.0*4.47e-5*X(5)+-1.0*1.07e-4*X(7);

1.0*0.4*rho*4.2850022315979^2+1.0*807362.4375+-1.0*0.4*rho*X(2)^2 + -1.0*X(9);

1.0*0.4*rho*4.2850022315979^2 + 1.0*807362.4375+-1.0*0.4*rho*X(3)^2+-1.0*X(10);

1.0*0.4*rho*4.2850022315979^2 + 1.0*807362.4375+-1.0*0.4*rho*X(4)^2+-1.0*X(11);

-1.0*0.4*rho*X(1)^2 + -1.0*X(8)+ 1.0*0.4*rho*X(4)^2 + 1.0*X(11);

-1.0*0.4*rho*X(1)^2 + -1.0*X(8) + 1.0*0.4*rho*X(5)^2 + 1.0*X(12);

-1.0*0.4*rho*X(1)^2 + -1*X(8) + 1.0*0.4*rho*X(6)^2 + 1.0*X(13);

-1.0*0.4*rho*X(6)^2 + -1.0*X(13) + 1.0*0.4*rho*X(2)^2 + 1.0*X(9);

-1.0*0.4*rho*X(6)^2 + -1.0*X(13) + 1.0*0.4*rho*X(7)^2 + 1.0*X(14);

1.0*0.4*rho*X(3)^2 + 1.0*X(10) + -1.0*0.4*rho*X(5)^2 + -1.0*X(12);

1.0*0.4*rho*X(3)^2 + 1.0*X(10) + -1.0*0.4*rho*X(7)^2 + -1.0*X(14)

];

end

options = optimset('Display','iter','TolX',1e-7,'MaxFunEvals',18000,'MaxIter',2200);

[Sol,fval,exitflag]=fsolve(@compare,X,options);

following error comes

No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function

values is not near zero, as measured by the default value of the function tolerance.

<stopping criteria details>

where X's are the variables

Please Guide!!!

Regards

Star Strider
on 10 Jun 2014

Edited: Star Strider
on 10 Jun 2014

You have to write your function so that all of your unknowns are in the same parameter vector.

So calling your parameter vector ‘B’:

B = [V(1) ... V(7) P(1) ... P(7)];

then replace V(1) with B(1), P(1) with B(8), and so forth.

If you intend ‘F’ to be an anonymous function, you have to write it as:

F = @(B,rho) [1.0*10.0*25+-1.0*17.0*B(2)+ ... + -1.0*0.4*rho*B(7)^2 + -1.0*B(14)];

(I abbreviated the function here.) Use the ‘Search’ and ‘Replace’ utilities in the MATLAB Editor to do this more easily.

Your call to fsolve is then:

[x,fval] = fsolve(@(B) F(B,rho),x0)

Your F function will get ‘rho’ from your workspace.

EDIT — Try using different starting values for ‘X’ that are reasonably close to what you expect them to be. Otherwise experiment with them. If it doesn’t converge on a solution after several attempts, it may not have a solution. If you believe it should, go back to your original equations and be sure you wrote ‘F’ correctly.

Marc
on 15 Jun 2014

Edited: Marc
on 15 Jun 2014

Taking Star Strider's approach, I compared "patternsearch" with "fsolve". For patternsearch, I used the following objective function:

fObj = sum(F.^2)

Called patternsearch and solve with the following initial guess...

xGuess = [1.0; 0.5; 0.25; 0.1; 1.2; 2.3; 3; 0.5;

2.0; 1.5; 1.2; 0.46; 0.9; 0.8; 2];

%xGuess = [10; 10; 10; 10; 10; 10; 10; 10;

% 10; 10; 10; 10; 10; 10; 10];

F = craxy14(xGuess)

options1 = optimset('Display','iter','TolX',1e-7,'MaxFunEvals',18000,'MaxIter',2200);

[Sol,fval,exitflag]=fsolve(@craxy14,xGuess,options1)

fvalComp = sum(fval.^2)

options = psoptimset('TolX', 1e-12, 'TolFun', 1e-10);

[Sol, fval, exitflag] = patternsearch(@craxy14_PS, xGuess,[],[],[],[],[],[],[],options)

And got the following output...

F =

0.0021850145660667

-0.0009486

0.0001117

-0.000363465

814604.93514992

814680.43514992

814701.73514992

-395.3

175.96

1716.4

-2014.9

1483.9

-549.96

-3574.3

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead. > In fsolve at 309 In tryCrazy at 13

First-Order Norm of

Iteration Func-count Residual optimality Lambda step

0 16 1.99105e+12 3.27e+08 0.01

1 41 1.48607e+12 6.51e+09 1e+07 36.218

2 58 1.04076e+12 2.68e+09 1e+08 30.8991

3 74 7.3865e+11 5.56e+09 1e+07 26.3164

4 91 1.36874e+11 8.44e+09 1e+08 42.257

5 107 3.31559e+09 9.86e+08 1e+07 13.2943

6 123 703959 2.58e+07 1e+06 2.72485

7 139 2.20032 1.47e+04 100000 0.0333549

8 155 0.00565597 3.26 10000 7.18966e-05

9 171 0.00565585 8.38e-05 1000 1.69513e-08

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient, but the vector of function values is not near zero as measured by the default value of the function tolerance.

Sol =

45.1305446907037

45.1305011994196

45.1305149725761

45.1305231544755

45.1305458382382

45.1305337039192

45.1305364903727

0.509518068564456

2.07974558905608

1.58247394623463

1.2870712557843

0.468086982642547

0.906189676429257

0.805586368498305

2

fval =

-0.0569063178351894

-0.0488177116737268

0.0033216051864278

-0.00482896878416497

5.23959542420016e-09

5.85573345368573e-09

4.49008474845414e-09

3.42615713577743e-09

-8.54356030366432e-11

5.20720910834882e-10

2.21098517272367e-09

-2.78552736432403e-10

2.18091139592147e-09

1.90836724200949e-09

exitflag =

-2

fvalComp =

0.00565584998315177

Optimization terminated: mesh size less than options.TolMesh.

Sol =

1

32

16.25

16.1

1.2

2.3

3

814306.935150146

405106.935150146

709081.935150146

711022.935149383

814130.935150108

812590.935150528

811106.935150909

2

fval =

0.00147856720654457

exitflag =

1

Not sure which one is "more" or "less" right.

Alex Sha
on 11 Dec 2019

Two of solutions:

1:

x1 0.0302626794484622

x2 2.44987629792448

x3 -3.17840769482201

x4 -0.0245615818144686

x5 -0.291871074861581

x6 0.479277650607576

x7 -1.20587090572179

x8 814706.568818013

x9 812306.177599867

x10 810666.024960118

x11 814706.693841399

x12 814672.859660183

x13 814615.052323371

x14 814125.285293413

2:

x1 0.168219021935448

x2 2.20358006851998

x3 1.00461250566195

x4 0.191813576695766

x5 0.564198756330943

x6 1.69971951063707

x7 0.18398593079529

x8 814695.616094183

x9 812764.629102568

x10 814303.236635307

x11 814692.218170638

x12 814579.607055261

x13 813551.316583983

x14 814693.394820827

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