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.