How to optimize k*x <= epsilon?

Hello Friends,

I want to optimize, i.e., find the optimal value of k in the following problem:

max k*x <= epsilon

How to find the maximum value of k for a given matrix x and some epsilon, say, 0.1?

I will appreciate any advise!

Answer 1

[Torsten]

Please state your problem more clearly.

k is a scalar and epsilon is a matrix with all elements equal to Epsilon, and you want to determine the maximum value of k such that k*x <= epsilon holds elementwise ?

In this case, the optimum k_opt is given by

k_opt = epsilon/max(x(:))

Best wishes

Torsten.