MATLAB: Solving simultaneous equations with fsolve

fsolve

Hello,

I was given the code:

xo=1 ;

fun=@(X) [sum(X)-2; X(2).^2 -X(3)-5 ; X(1)+X(3.)^3-2];

x = fsolve(fun,xo)

But when I try to run it, I get the following error:

Index exceeds matrix dimensions.

Error in @(X)[sum(X)-2;X(2).^2,-X(3)-5;X(1)+X(3.)^3-2]

Error in fsolve (line 241) fuser = feval(funfcn{3},x,varargin{:});

Error in test2 (line 4) x = fsolve(fun,xo)

Caused by: Failure in initial user-supplied objective function evaluation. FSOLVE cannot continue.

Can someone please explain why this isnt working?

Thanks!

Mike

Best Answer

Your problem is 3-dimensional, but the initial guess you gave x0=1 is only 1-dimensional.

Related Solutions

MATLAB: Problems with fmincon, how to solve

Your problem is convex, so you can use the CVX package if you want. Also, the solution should be the global minimum; not a local minimum. To use fmincon, do the following:

Equality/nonEquality constraint:

function [c,ceq]=mycon(x)
c(1) = x(1)^2 + x(2)^2 - 4*x(1) - 3*x(2) + 5;
c(2) = -x(1)^2 - x(2)^2 + 4*x(1) + 3*x(2) - 6; % notice the fixed typo
ceq = 2*x(1)^2 + 2*x(2)^2 - 3*x(1) - 3*x(2) - 2; 
end

Construct the problem and call fmincon:

clc
clear all
Aeq=[]; 
beq=[]; 
A=[]; 
b=[]; 
% if you are not sure that vector x is within lb and ub do not restrict it
lb = []; %lb=[-3,-3]; 
ub = []; %ub=[3,3]; % 
x0=[4,4];
myObj = @(x) x(1)^2 + x(2)^2 - 5*x(1) - 6*x(2) + 15;
nonlcon = @mycon;
options = optimoptions('fmincon','Algorithm','sqp','Display','iter-detailed','MaxFunctionEvaluations',100000, 'MaxIterations',2000, 'OptimalityTolerance' ,1e-10);
[x,cost] = fmincon(myObj,x0,A,b,Aeq,beq,lb,ub,nonlcon)

Output (global minimum):


Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
<stopping criteria details>
x =
    1.6450    1.9007
cost =
    1.6896

MATLAB: How do you use fsolve to solve simultaneous equations

You need to rewrite as F(X)=0 where X is your vector of unknowns

 fun=@(X) [sum(X)-2; X(2)^2 -X(3)-5 ; X(1)+X(3)^3-2];

Then

x = fsolve(fun,x0)

where x0 is your initial guess. There are other input/output arguments that you can use to refine the behavior of FSOLVE (see "doc fsolve").

Best Answer

Related Solutions

MATLAB: Problems with fmincon, how to solve

MATLAB: How do you use fsolve to solve simultaneous equations

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