Asked by Clarisha Nijman
on 26 Nov 2018

Hello,

Given:

A=[4 3; -1 7; 5 9; 2 4];

x=[x1;x2];

b=[b1; b2; b3; b4];

How can I maximize the linear system of equations: Ax=b?

Answer by Matt J
on 26 Nov 2018

Edited by Matt J
on 27 Nov 2018

Accepted Answer

Clarisha Nijman
on 30 Nov 2018

The last line of the code:

"[OptArgum, optimalVal] = fminimax(@(x) Cs*x,x0,Aleq,bleq(:),Aeq.',beq,lb,ub); "

is underlined (red), and the comment says:

"Function definition in a script must appear at the end of the file. Move statements to before the function definitions".

Matt J
on 30 Nov 2018

Runs fine for me. Here is my complete implementation.

C=[ 0.0038 0.0038 0.0038 0.0038

0.0037 0.0037 0.0037 0.0037

0.0036 0.0036 0.0036 0.0036

0.0034 0.0034 0.0035 0.0035

0.0033 0.0033 0.0034 0.0034

0.0032 0.0032 0.0033 0.0033

0.0031 0.0031 0.0032 0.0033

0.0029 0.0029 0.0031 0.0031

0.0028 0.0028 0.0029 0.0028

0.0027 0.0027 0.0024 0.0023];

A1=C(:,2:end);

A2=-C(:,2:end);

Aleq=[A1;A2];

%The less equal RHS

bleq=[C(:,1) -C(:,1)];

Aeq=ones(3,1);

beq=1;

lb=zeros(3,1);

ub=[];

%initial guess

x0=0.1*rand(3,1);

%Defining the objective function

Cs=C(:,2:4);

[OptArgum, optimalVal] = fminimax(@(x) Cs*x,x0,Aleq,bleq(:),Aeq.',beq,lb,ub);

Clarisha Nijman
on 1 Dec 2018

Ok I see,

Two questions more;

Can you give me some explanation about the first argument of the fminmax code: @(x) Cs*x

Can you give me some explanation about the output? Should I change the tolerance of choose a larger rand initial guess? The output says:

Converged to an infeasible point.

fminimax stopped because the predicted change in the objective function

is less than the default value of the function tolerance but constraints

are not satisfied to within the default value of the constraint tolerance.

<stopping criteria details>

Optimization stopped because the predicted change in the objective function, 0.000000e+00,

is less than options.FunctionTolerance = 1.000000e-06, but the maximum constraint violation,

1.093094e+00, exceeds options.ConstraintTolerance = 1.000000e-06.

Optimization Metric Options

abs(steplength*directional derivative) = 0.00e+00 FunctionTolerance = 1e-06 (default)

max(constraint violation) = 1.09e+00 ConstraintTolerance = 1e-06 (default)

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## 4 Comments

## Matt J (view profile)

Direct link to this comment:https://it.mathworks.com/matlabcentral/answers/432056-how-to-maximize-system-of-linear-equations#comment_642546

## Clarisha Nijman (view profile)

Direct link to this comment:https://it.mathworks.com/matlabcentral/answers/432056-how-to-maximize-system-of-linear-equations#comment_642568

## Matt J (view profile)

Direct link to this comment:https://it.mathworks.com/matlabcentral/answers/432056-how-to-maximize-system-of-linear-equations#comment_642624

## Clarisha Nijman (view profile)

Direct link to this comment:https://it.mathworks.com/matlabcentral/answers/432056-how-to-maximize-system-of-linear-equations#comment_642655

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