Is there an algorithm or an efficient way to solve the following equation

$S=

frac{

begin{bmatrix}

R_{1} & . & . & R_{n}\

end{bmatrix}

begin{bmatrix}

P_{1}\

. \

. \

P_{n}\

end{bmatrix}

}{

Maximumleft(

begin{bmatrix}

D_{1,1} & . & . & D_{1,n}\

. & . & . & .\

. & . & . & .\

D_{m,1} & . & . & D_{m,n}\

end{bmatrix}

begin{bmatrix}

P_{1}\

. \

. \

P_{n}\

end{bmatrix}right)}$

With known values for:

- $D$ is $m$ x $n$ Matrix
- $R$ is $n$ x $1$ Vector

Need to calculate the values of:

- $P$ which is $1$ x $n$ Vector made of non-negative numbers, sum of all is 1.0

To achieve maximum value for scalar $S$, however its value is not important.

Note in the above equation $D P$ produces a $n x 1$ vector, and $Maximum(D P)$ represents highest numeric value from it.