MATLAB: Doubly stochastic matrix in linear programming

doubly stochastic matrixlinear programming

How may I get the vector x by using linprog(f,A,b), where b=Wy(y is a known vector) and W is all possible doubly stochastic matrix? Or other methods will work for lp given constraints involve doubly stochastic matrix, especially if W is high dimensional and enumeration seems infeasible?

Best Answer

You mean how you can formulate the above problem for linprog ?
min: f'x
s.c.
A*x-Z*y=0
sum_i z_ij = 1
sum_j z_ij = 1
0 <= z_ij <= 1
Or what exactly are you asking for ?
Best wishes
Torsten.
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