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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 61E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0ff8323-0fa0-42e7-8175-4472db174a53%2F48386a90-976c-468b-817c-f512d109d4b2%2Flkpt98_processed.jpeg&w=3840&q=75)
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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