Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Suppose f is differentiable everywhere. Show that if æ* is a local minimizer for f, Vf(x*) = 0. Note that we are not assuming the gradient map is continuous.

Suppose f is differentiable everywhere. Show that if æ* is a local minimizer for f, Vf(x*) = 0. Note that we are not assuming the gradient map is continuous.

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
See similar textbooks
icon
Related questions
Question
100%

Plz solve within 30min I vill give definitely upvote and vill give positive feedback thank you 

Exercise 1.2 ( : Let f: R" → R. (a) Suppose f is differentiable everywhere. Show that if a* is a local minimizer for f, Vf(x) = 0. Note that we are not assuming the gradient map is continuous. (b) Suppose f is twice continuously differentiable. By defining (n) formula (1) = (0) + - $¹(0) + ² * $"(t) dt da. Hence, show that for any a, s € R" f(x+ns), justify the \ƒ(x + s) − ƒ(x) − g(x)¹s − ½s¹H(x)s| ≤ 79||$||2, whenever f has a Lipschitz continuous Hessian with Lipschitz constant on S.
Transcribed Image Text:Exercise 1.2 ( : Let f: R" → R. (a) Suppose f is differentiable everywhere. Show that if a* is a local minimizer for f, Vf(x) = 0. Note that we are not assuming the gradient map is continuous. (b) Suppose f is twice continuously differentiable. By defining (n) formula (1) = (0) + - $¹(0) + ² * $"(t) dt da. Hence, show that for any a, s € R" f(x+ns), justify the \ƒ(x + s) − ƒ(x) − g(x)¹s − ½s¹H(x)s| ≤ 79||$||2, whenever f has a Lipschitz continuous Hessian with Lipschitz constant on S.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS