Show that the function: f(t)=−logdetZ−sum_i=1^n log(1+t lambdai)−trace((Z+tV)^(−1)Y) is concave in t.

Demarion Ortega

Demarion Ortega

Answered question

2022-11-05

Show that the function:
f ( t ) = log det Z i = 1 n log ( 1 + t λ i ) trace ( ( Z + t V ) 1 Y )
is concave in t.

Answer & Explanation

tektonikafrs

tektonikafrs

Beginner2022-11-06Added 15 answers

Hint for the trace term:
1)For fixed Y, the trace of X Y is linear, with derivative Y.
2)The derivative A 1 with respect to t is A 1 d A d t A 1 .
3)Combine 1) and 2) using the chain rule.

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