An objective function model is given by m_k(x) = x_1^2 + Find the two-dimensional subspace 5x 2^2 + x 3^2 + x_4^2 + 4x_4. minimizer for m_k at x_k-(1,1,1,1) with delta_k = 1/2. global minimizer? What is the
An objective function model is given by m_k(x) = x_1^2 + Find the two-dimensional subspace 5x 2^2 + x 3^2 + x_4^2 + 4x_4. minimizer for m_k at x_k-(1,1,1,1) with delta_k = 1/2. global minimizer? What is the
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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![Ans
5. The gradient is p_1 = g = [6,8,40,2,0]^T, and the Hessian is:
[2 0 0 0 0]
[0 2 6 0 0]
[0 6 34 0 0]
[0 0
0 2 0]
5.
[00 002],
We can
so the second direction is p_2 = -B^-1 g = [-3,-1,-1,-1,0] ^T.
assume that the minimizer is at the border of the trust region, and the
result is p = 0.0046*p_1 + 0.1621*p_2= [-0.4587 -0.1253 0.0219 -0.1529
0]^T, giving a minimizer of [0.5413 0.8747 1.0219 0.8471 11^T.
The global minimizer can be found by rewriting f(x) = (x_1+2)^2 - 4 +
(x_2+3x_3)^2 + 8x_3^2 + x^4^2 + (x_5-1)^2 - 1, so that the minimizer is [-
2,0,0,0,1].
Question
s) An objective function model is given by m_k (x) = x_1^2 +
4x 1 + x_2^2 + 17x_3^2 + x_4^2 + x_5^2 + 6x_2x_3 - 2x 5. Find the
two-dimensional subspace minimizer for m_k at x_k=(1,1,1,1,1) with
delta_k= 1/2. What is the global minimizer?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a9783c8-0cb2-4e1c-b8cd-815eb34093aa%2Fa2549048-4f13-43e9-bd7d-84e7bb3645c2%2F8nivwyr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ans
5. The gradient is p_1 = g = [6,8,40,2,0]^T, and the Hessian is:
[2 0 0 0 0]
[0 2 6 0 0]
[0 6 34 0 0]
[0 0
0 2 0]
5.
[00 002],
We can
so the second direction is p_2 = -B^-1 g = [-3,-1,-1,-1,0] ^T.
assume that the minimizer is at the border of the trust region, and the
result is p = 0.0046*p_1 + 0.1621*p_2= [-0.4587 -0.1253 0.0219 -0.1529
0]^T, giving a minimizer of [0.5413 0.8747 1.0219 0.8471 11^T.
The global minimizer can be found by rewriting f(x) = (x_1+2)^2 - 4 +
(x_2+3x_3)^2 + 8x_3^2 + x^4^2 + (x_5-1)^2 - 1, so that the minimizer is [-
2,0,0,0,1].
Question
s) An objective function model is given by m_k (x) = x_1^2 +
4x 1 + x_2^2 + 17x_3^2 + x_4^2 + x_5^2 + 6x_2x_3 - 2x 5. Find the
two-dimensional subspace minimizer for m_k at x_k=(1,1,1,1,1) with
delta_k= 1/2. What is the global minimizer?
![5.
An objective function model is given by m_k (x) = x_1^2 +
Find the two-dimensional subspace
5x 2^2 + x 3^2 + x_4^2 + 4x 4.
minimizer for m_k at x_k= (1,1,1,1) with delta_k= 1/2.
global minimizer?
What is the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a9783c8-0cb2-4e1c-b8cd-815eb34093aa%2Fa2549048-4f13-43e9-bd7d-84e7bb3645c2%2Fvfgfwa5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.
An objective function model is given by m_k (x) = x_1^2 +
Find the two-dimensional subspace
5x 2^2 + x 3^2 + x_4^2 + 4x 4.
minimizer for m_k at x_k= (1,1,1,1) with delta_k= 1/2.
global minimizer?
What is the
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