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Let f RR be a convex function. In this question, we want to f(x) ≤ M for all x, then f is a constant function. prove that if M ER and (a) Prove that f(x+t(y - x)) ≥ ƒ(x) + t(ƒ(ÿ) − ƒ(x)) for all , ÿ € R” and t ≥ 1.

Let f RR be a convex function. In this question, we want to f(x) ≤ M for all x, then f is a constant function. prove that if M ER and (a) Prove that f(x+t(y - x)) ≥ ƒ(x) + t(ƒ(ÿ) − ƒ(x)) for all , ÿ € R” and t ≥ 1.

Advanced Engineering Mathematics
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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Topic: Mathematics - Optimization Techniques 

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Let f RR be a convex function. In this question, we want to f(x) ≤ M for all x, then f is a constant function. prove that if M ER and (a) Prove that f(x+t(y - x)) ≥ ƒ(x) + t(ƒ(ÿ) − ƒ(x)) for all , ÿ € R" and t ≥ 1.
Transcribed Image Text:Let f RR be a convex function. In this question, we want to f(x) ≤ M for all x, then f is a constant function. prove that if M ER and (a) Prove that f(x+t(y - x)) ≥ ƒ(x) + t(ƒ(ÿ) − ƒ(x)) for all , ÿ € R" and t ≥ 1.
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