Linear programming with equality constraints

  Consider the following classical optimization problem

where A and C are matrices and e, b and d are vectors with appropriate dimensions. Here the sign is to be understood elementwise.

This problem can be formulated in LMITOOL as follows:

function [LME,LMI,OBJ]=linprog_eval(XLIST)
 [x]=XLIST(:)
 [m,n]=size(A)
 LME=C*x+d
 LMI=list()
 tmp=A*x+b 
 for i=1:m
    LMI(i)=tmp(i)
 end
 OBJ=e'*x

and solved in Scilab by (assuming A, C, e, b and d and an initial guess x0 exist in the environment):

--> x=lmisolver(x0,linprog_eval)