2. For the matrix Q = consider the function f : R² → R below: 7 x²Qx − f(x1, x2) = x² Qx — [−16, 14]x +3 - a) Find a point x* that satisfies FONC (Vƒ (x*) = 0) for f. b) Is x a strict local minimizer of f? You can use SOSC or SONC. c) Find the level set off at the origin and sketch its graph in R². d) Find the unit direction vector of greatest decrease of f at the origin.
2. For the matrix Q = consider the function f : R² → R below: 7 x²Qx − f(x1, x2) = x² Qx — [−16, 14]x +3 - a) Find a point x* that satisfies FONC (Vƒ (x*) = 0) for f. b) Is x a strict local minimizer of f? You can use SOSC or SONC. c) Find the level set off at the origin and sketch its graph in R². d) Find the unit direction vector of greatest decrease of f at the origin.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 20EQ
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optimization theory
![2. For the matrix Q
=
consider the function f : R² → R below:
7
x²Qx −
f(x1, x2) = x² Qx — [−16, 14]x +3
-
a) Find a point x* that satisfies FONC (Vƒ (x*) = 0) for f.
b) Is x a strict local minimizer of f? You can use SOSC or SONC.
c) Find the level set off at the origin and sketch its graph in R².
d) Find the unit direction vector of greatest decrease of f at the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cd79f82-3730-49d1-8559-a01cc4e6e9ca%2F936a2510-6c3a-4ac8-84ec-67ad7946ddcd%2Fps1hdp7_processed.png&w=3840&q=75)
Transcribed Image Text:2. For the matrix Q
=
consider the function f : R² → R below:
7
x²Qx −
f(x1, x2) = x² Qx — [−16, 14]x +3
-
a) Find a point x* that satisfies FONC (Vƒ (x*) = 0) for f.
b) Is x a strict local minimizer of f? You can use SOSC or SONC.
c) Find the level set off at the origin and sketch its graph in R².
d) Find the unit direction vector of greatest decrease of f at the origin.
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