I'm getting an error related to fmincon

Question is this;

My matlab code is as follows:

%Define Matrices 
>> M = magic(5);
>> P = pascal (5);

% Define the variable x
>> syms x

%Define the given matrix A
>> A = x*M + (1-x)*P;
%Define the eigenvalue lambda as y;
>> syms y

%Find determinant of |A - lambda * I|

>> D = det (A - y*eye(5))

%Define Objective function 

objective = @(y) y

%And Define the constraint

constraint = @(x,y) (-1)*D

%initial value x0 = (0:0.001:1);

%Minimization problem solving 
x = fmincon(objective, constraint, x0)

I get this error;

Error using fmincon (line 221)
FMINCON requires the following inputs to be of data type double: 'X0'.

If I use another function: fminsearch

x = fminsearch(objective, constraint, x0)

In this case I get the following error:

Error using fminsearch (line 96)
FMINSEARCH accepts inputs only of data type double.

How can I deal with these errors ? Where is my mistake? How can I correct them?

[Torsten]

What do mean by "largest eigenvalue" ? The largest real-valued eigenvalue or the eigenvalue largest in magnitude ?

[Zeynep Toprak]

I guess you asked behind its math. Okay, I can explain as follows:

[Zeynep Toprak]

Is this explanation and solution enough?

Answer 1

[Ameer Hamza]

This is an example with fmincon

M = magic(5);
P = pascal (5);

f = @(x) max(abs(eig(x*M + (1-x)*P)));
x_sol = fmincon(f, rand, [], [], [], [], 0, 1);

[Zeynep Toprak]

In fact, this is what I tried to do . Many many thanks :))

[Zeynep Toprak]

by the way, please explain why you put " rand, [], [], [], [], 0, 1. " Can you explain these inputs please.

[Zeynep Toprak]

And also, it doesnt give a result. It says this.

[Ameer Hamza]

The second input is a starting point for the algorithm. It is best if it is closer to the actual solution since it will help the algorithm to converge quickly, but not necessary, and you can input any number. I use rand(), which generates a random number between 0 and 1. The next 4 inputs are used to specify linear equality and inequality constraints. Since your problem don;t have any, therefore, I wrote [] at there place. The last two numbers are lower and upper bound on optimization variables.

[Ameer Hamza]

What is the value of x_sol? What MATLAB release are you using. MATLAB recently made some improvements in fmincon, maybe in previous release, fmincon is not able to find optimal solution.

[Zeynep Toprak]

x_sol = 0.7960.

[Zeynep Toprak]

This is correct when I compare it with what I solve by other ways.

[Zeynep Toprak]

Many thanks again :)

[Ameer Hamza]

Glad to be of help.

Answer 2

[Torsten]

If you mean the eigenvalue largest in magnitude, this should give you a start.

Incorporating fmincon can automatize the search for an optimal x.

M=magic(5);

P=pascal(5);

A=@(x) x*M+(1-x)*P;

x=0:0.02:1;

for i=1:numel(x)

d(i) = abs( eigs(A(x(i)),1) );

end

[dmin,idd] = min(d);

x(idd) %show x for which eigenvalue largest in magnitude is minimum

[Zeynep Toprak]

Thanks a lot, but this code gives error again. I dont understand why? I only correct this paranthesis

d(i) = eigs(A(x(i),1));

But, Again I see error.

[Zeynep Toprak]

[Torsten]

The error was corrected in the meantime.

[Zeynep Toprak]

yeah, it works!! Many many thankss!! Take care of yourself! :))