a) Let f(r) be a function f : R" → R not necessarily differentiable. Define each of the following: (i) an unconstrained local minimizer; (ii) a strict local minimizer; and (iii) an isolated local minimizer.
a) Let f(r) be a function f : R" → R not necessarily differentiable. Define each of the following: (i) an unconstrained local minimizer; (ii) a strict local minimizer; and (iii) an isolated local minimizer.
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:(a) Let f(x) be a function f : R" + R not necessarily differentiable. Define each of the
following: (i) an unconstrained local minimizer; (ii) a strict local minimizer; and (iii)
an isolated local minimizer.
(b) Discuss the properties of the following functions with reference to the existence of: a lo-
cal unconstrained minimizer/maximizer; a strict local unconstrained minimizer/maximizer;
an isolated local unconstrained minimizer/maximizer; and a global minimizer/maximizer.
(i)
1 if r +1
* if x = 1.
f(x) =
(ii)
x +2 if x <-1
f (x) = { 1
if –1 <x < 1
2 - x if x > 1.
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