Suppose f(): R" → R is a function. Consider the optimization problem (P) min f(x) over XER". #1) (a) When does f(-) have a gradient? (b) When is f(-) = C¹? (c) When is f(-) € C²?
Suppose f(): R" → R is a function. Consider the optimization problem (P) min f(x) over XER". #1) (a) When does f(-) have a gradient? (b) When is f(-) = C¹? (c) When is f(-) € C²?
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:Suppose f(): R" → R is a function. Consider the optimization problem
(P)
min f(x) over XER".
#1) (a) When does f(-) have a gradient? (b) When is f(-) € C¹? (c) When is f(-) € C²?
Expert Solution
Step 1
Given f: R^n --> R is a function
We have to minimise f.
a) For that f should have gradient in every direction, i.e grad(f) must exist.
If all the directional derivatives of f exist for every direction. Then grad(f) exist.
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