How to solve an equation of the form A (matrix) x(vector) = b(vector) and a constant c where I have to find x and c, and x is only positive?

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German Preciat Gonzalez 2016-12-4

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回答： Star Strider 2016-12-4

Hi, I have a matrix A

A =[1 1 2 2 0 0;
1 2 2 0 0;
0 0 1 0 0;
0 0 1 0 0;
0 0 0 0 0;
0 0 0 0 0;
0 0 0 1 0;
0 0 0 1 0;
0 0 0 1 0;
0 1 1 1 0;
0 1 1 1 0;
0 2 0 0 1;
0 2 0 0 1];

and a vector b

b = [64.20; 42.60; 14.60; 5.75; 30.40; 27.20; 36.50; 25.40; 40.60; 38.90; 15.50; 38.40; 35.30];

if I use linesolve, I have

but negative values are nor realistic, I was planning to use linear programming but I'm not sure if is the way to go since I also need to have a constant (which can be negative) so I can have

Axc=b

Can you recommend me something?

Thanks!

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Answer 1

Star Strider 2016-12-4

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在 MATLAB Online 中打开

If you want to avoid negative parameters, use the lsqnonneg function.

Example:

x = lsqnonneg(A,b)
x =
          9.6
       36.306
            0
       3.7469
       1.0813
         8.05

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Answer 2

KSSV 2016-12-4

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Doc mldivide

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German Preciat Gonzalez 2016-12-4

that is why I want to use a constant C that multiplies vector x so the vector x can have only positive values: Axc=b

KSSV 2016-12-4

C = [1 1 -1 1 1 1 1]';

But you should do element by element .* multiplication.

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How to solve an equation of the form A (matrix) x(vector) = b(vector) and a constant c where I have to find x and c, and x is only positive?

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How to solve an equation of the form A (matrix) x(vector) = b(vector) and a constant c where I have to find x and c, and x is only positive?

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