How to arrange the constraints shape to A matrix and b constants automatically ( Ax <= b)??

Hi. I'm not good at MATLAB so please help me^^

I want to solve LP problem using "linprog",

so I have to make inequality constraints to A matrix and b constants. (Ax <= b)

And my inequality constraint's variables are mixed each other, so I have to arrange the constraints.

For example,

x1 + x2 <= x3 + x4 + 1 ;  % constraint 1
X3 <= x1 + 10 ;  % constraint 2
x2 + x4 <= 7 ;  % constraint 3

In this situation, how can I make shape "Ax <= b" automatically??

It means I don't have to code one by one.

[Sanush]

Rearrange your constraint

Px1 <= Qx2 + c

(P - Q - c)*(x1', x2', 1)' <= 0

% for x1 + x2 <= x3 + x4 + 1
P = x1 + x2
Q = x3 + x4 + 1

% As Ax <= b
A = P - Q
b = zeros(size(A,1),1)

Answer 1

[Matt J]

Using the problem-based solvers, you do not have to build things in matrix form, e.g.,

x=optimvar('x',4,'LowerBound',0,'UpperBound',20);

con(1)=x(1) + x(2) <= x(3) + x(4) + 1 ;  % constraint 1
con(2)=x(3) <= x(1) + 10 ;  % constraint 2
con(3)=x(2) + x(4) <= 7 ;  % constraint 3

sol=solve( optimproblem('Objective',-sum(x),'Constraints',con) )

Solving problem using linprog.

Optimal solution found.

sol = struct with fields:
    x: [4×1 double]

However, if you really must have the matrices, then you can use prob2matrices,

https://www.mathworks.com/matlabcentral/fileexchange/74481-prob2matrices-a-selective-version-of-prob2struct

p=prob2matrices({x},'Constraints',con)

p = struct with fields:
    intcon: []
        lb: [4×1 double]
        ub: [4×1 double]
     Aineq: [3×4 double]
     bineq: [3×1 double]
       Aeq: []
       beq: []

[연승 김]

Ok. Thank you for your kind and sorry I'm late.

Answer 2

[Chunru]

% Let x = [x1; x2; x3; x4]

% x1 + x2 <= x3 + x4 + 1 ;  % constraint 1
% =>   [1 1 -1 -1]*x <= 1

% X3 <= x1 + 10 ;  % constraint 2
% => [-1 0 1 0]*x <= 10

% x2 + x4 <= 7 ;  % constraint 3
% =>  [0 1 0 1]*x <=7

% Putting together
%  [ 1  1 -1 -1]       [ 1 ]
%  |-1  0  1  0| * x <=|10 ] 
%  [ 0  1  0  1]       [ 7 ]
%
% Therefore, you can specify A and b as follows
A = [1  1 -1 -1;  -1  0  1  0;  0  1  0  1];
b = [1; 10; 7];

[연승 김]

I understant what you mean, but my queation is different.

The inequality constraints make automatically by iteration,

so I want to creat A matrix automatically...

Do you understant what I mean??

I'm sorry that confusing you...

[Chunru]

No. I don't understand you. Can you explain with examples?