Proving that exp(−x^2−y^2) is a strictly quasi-concave function

Jadon Johnson

Jadon Johnson

Answered question

2022-11-02

Proving that exp ( x 2 y 2 ) is a strictly quasi-concave function

Answer & Explanation

dilettato5t1

dilettato5t1

Beginner2022-11-03Added 25 answers

The logarithm is a strictly increasing monotonic function, so if a > b then log a > log b and vice-versa. Take logarithms then
log ( e x 2 y 2 ) = 2 ( log x + log y )
Using just one dimension, suppose that the maximum is at x 1 then
log exp ( λ x 1 + ( 1 λ ) x 2 ) 2 = 2 ( λ x 1 + ( 1 λ ) x 2 ) > 2 x 1
by the usual inequalities.

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