Let A C Rª be a convex set. f : A → R is a strictly quasi-concave function if and only if for any a E (0,1) and any x1, x2 E A such that x1 + x2, ƒ (ax1+(1– a)x2) > min {f (x1), f (x2)}. Please prove that a local maximum point of a strictly quasi-concave function must also be a global maximum point. (This is a different variation of Theorem 1 in Week 4, so you cannot prove this statement by directly citing that Theorem.)
Let A C Rª be a convex set. f : A → R is a strictly quasi-concave function if and only if for any a E (0,1) and any x1, x2 E A such that x1 + x2, ƒ (ax1+(1– a)x2) > min {f (x1), f (x2)}. Please prove that a local maximum point of a strictly quasi-concave function must also be a global maximum point. (This is a different variation of Theorem 1 in Week 4, so you cannot prove this statement by directly citing that Theorem.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let A C R" be a convex set. f : A → R is a strictly quasi-concave function if
and only if for any a e (0,1) and any x1, x2 E A such that x1 x2, ƒ (ax1+(1 – a)x2) >
min {f (x1), f (x2)}.
Please prove that a local maximum point of a strictly quasi-concave function must also be a
global maximum point. (This is a different variation of Theorem 1 in Week 4, so you cannot
prove this statement by directly citing that Theorem.)
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