MATLAB: How to set the sum of the absolute value of variables as inequality matrix and vector in linear programming

absolute valueconstrainslinprogMATLABprogramming

I am trying to solve a linear program with command "linprog". The inequality constrains has a sum of varaibles. e.g. I have 3 variable. x1,x2,x3.

The constrain should be like "abs(x1)+abs(x2)+abs(x3)<=2";

How to set this constrains in matlab?

I had read the link of two variables problem. But I can't figure out the rule of it. I can't derive the 3 case from it, either. Could anyone give me some suggestions? That will be very appreciated.

Best Answer

You can intruduce slack variables y1, y2, y3

x1 <= y1 and x1 >= -y1
x2 <= y2 and x2 >= -y2
x3 <= y3 and x3 >= -y3
y1+y2+y3 <= 2

Formulate your LP with

X:=[x1,x2,x3,y1,y2,y3]'

and the above constraints

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MATLAB: Trying to make a piecewise function that isn’t for graphing or using the piecewise function itself

Use logical indexing on both sides of the assignment. E.g.,

function y = project2Tester(x)
  y = zeros(size(x));
    
  x1 = (x <= -1);
  y(x1) = log(abs(x(x1)));
  x2 = (-1 < x & x < 0);
  y(x2) = abs(x(x2));
  x3 = (0 <= x & x < 1);
  y(x3) = x(x3);
  x4 = (x >= 1);
  y(x4) = log(x(x4));
  y(~(x1 | x2 | x3 | x4)) = 0;  % not really needed since you initialized y to 0's
end

MATLAB: GA algorithm toolbox (define constraint)

This kind of system can be programmed by introducing up to 4 new integer variables, with the logical conditions

x1 == x6 * x4
x1 == x7 * x5
x2 == x8 * x4
x2 == x9 * x5

You would then follow that by reducing the original equations, replacing each x1 by x6 * x4 and each x2 by x8 * x4 everywhere the equations,

Then you would add the nonlinear equality constraints

x6 * x4 - x7 * x5
x8 * x4 - x9 * x5

The list of variables would be x3, x4, x5, x6, x7, x8, x9 with x4 through x9 all integer variables (so x3 is the only non-integer variable.)

I know your original list did not require x5 to be integer, but your integer constraints on the other variables require that x5 be integer, I figure.

Best Answer

Related Solutions

MATLAB: Trying to make a piecewise function that isn’t for graphing or using the piecewise function itself

MATLAB: GA algorithm toolbox (define constraint)

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