artificial intelligence – Find optimal Vector for a dataset equation problem

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.