L1 Norm for a linear system

Hi All,

I am trying to write an m-file for a function that returns L1 norm for a linear system using linprog (linear programming). I wrote the code below but it’s not working. I don’t know how to declare x as an unknown vector variable. The 2nd line gives me an error message which states “Not enough input arguments.”

Any help is highly appreciated and thanks in advance. EK

function n = lpaxb(Aeq,beq

n = norm((Aeq*x-beq),1)

x = linprog('lpaxb.m', n, A, b, Aeq,beq)

End

Answer 1

[Walter Roberson]

I see no evidence in the current documentation that linprog can be invoked with a string as its first argument.

If the string is intended to represent a "solver", then you need to pass in a problem structure, which is a structure with fields listed in the documentation under "Input Arguments". Note that if the string is a solver, it should be a function name, not the name of a .m file. With the lack of information about the "solver" field, it could be that "solver" needs to be literally 'linprog' .

I see no input field that I can match to your "n". If your "n" is intended to be a parameter to your chosen solver, then I cannot tell from the documentation whether there is a way to pass it in explicitly.

[EK]

First of all, thank you for your input. Let me say at the outset that I am new to Mat lab and have very little experience with it. The code I posted was my best imitation of an m-file to generate a simple m-file that calculates L-1 for a linear equality system of equations. I know my variables are not well defined and correctly passed in.

I thought if I execute n=lpaxb(Aeq, beq), then it passes the two variables to n, the 2nd statement, as the objective function, which in turn passes it to x which returns the solution in terms of L-1

I know I have a problem with the 2nd statement that I don’t know how to fix. It seems to me if that statement is correct, then the third statement is correct judging from what I read about linprog. Any modification of suggestion of my code is highly appreciated. Thanks again. EK

[Walter Roberson]

You cannot use linprog() to minimize functions such as lpaxb. The first argument you pass to linprog() must be a vector or matrix. The parameter will be matrix-multiplied by the current vector of values ("x") and linprog() will be attempting to find the "x" vector that makes the output result zeros.

I do not know if there are useful alternatives designed for linear programming. You might have to use a minimizer such as fmincon().