Consider the optimization problem c(p)=min_x sum_i=1^n x_ip_i subject to f(x)>=1 where f:R_+^n|->R is increasing and concave.

spasiocuo43

spasiocuo43

Answered question

2022-11-18

Consider the optimization problem
c ( p ) = min x i = 1 n x i p i
subject to f ( x ) 1 where f : R + n R is increasing and concave.

Answer & Explanation

Sean Sutton

Sean Sutton

Beginner2022-11-19Added 17 answers

Notice that since f is increasing, p i 0 for all i; otherwise we do not have the solution for problem. Then at the optimal solution x ( p ), we must have f ( x ( p ) ) = 1. Using this remark, one sufficient condition for c ( p ) is strictly concave is that f is strictly concave.

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