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Given a matrix A, $A$, each element A_i,j >= 0$A_{i,j} \geq 0$, find the vector x $\vec x$ that maximizes the minimum element in b $\vec b$ ($\vec b = Ax)A \vec x$). Note that this is not a linear equation system as I don't know b$\vec b$.

Extra contraints on the solution are x >= 0$x_i \geq 0$, and sum(x) $\sum x_i = 11$.

Is this possible to solve, and if so, how? Can it have 0 or more than one solution?

2 added 9 characters in body; added 8 characters in body

Given a matrix A, A each element A_i,j >= 0, find the vector x that maximizes the minimum element in b (b = Ax). Note that this is not a linear equation system as I don't know b.

Extra contraints on the solution are x >= 0, and sum(x) = 1.

Is this possible to solve, and if so, how? Can it have 0 or more than one solution?

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# For Ax = b, x and b unknown vectors, how do I solve the x that maximizes min(b_i)?

Given a matrix A, A >= 0, find the vector x that maximizes the minimum element in b (b = Ax). Note that this is not a linear equation system as I don't know b.

Extra contraints on the solution are x >= 0, and sum(x) = 1.

Is this possible to solve, and if so, how? Can it have 0 or more than one solution?