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Math-484 Homework #10 (Penatly methods and iterative methods)
I will nish the homework before 10am Dec 5. If I spot a mathematical mistake I will let the
lecturer know as soon as possible.
I will writ
Math-484 Homework #2 (semidenite and coercive)
I will nish the homework before 10am Sep 12. If I spot a mathematical mistake I will
let the lecturer know as soon as possible.
I will write clearly and
Math-484 Homework #6 (Least squares)
I will nish the homework before 10am Oct 17. If I spot a mathematical mistake I will let
the lecturer know as soon as possible.
I will write clearly and neatly as
Math-484 Homework #3 (convex sets and functions)
I will nish the homework before 10am Sep 19. If I spot a mathematical mistake I will
let the lecturer know as soon as possible.
I will write clearly an
Math-484 Homework #10 (penalty method)
I will nish the homework before 11am Nov 13. If I spot a mathematical mistake I will let
the lecturer know as soon as possible.
I will write clearly and neatly a
Math 484: Topics Covered on the Final Exam
Misha Lavrov
December 10, 2017
The final exam will be cumulative, but with added focus on the material covered after Thanksgiving
(which we have not had an e
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #8
Fall 2017
Due Friday, November 10
1. Solve the convex program
minimize
2
x4 + y 4
subject to
8x + y = 17
(x,y)R
specifically by finding the d
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #7
Fall 2017
Due Friday, November 3
1. Use the KarushKuhnTucker theorem to solve the optimization problem
x2 + y 2 4x 4y
minimize
(x,y)R2
subjec
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #10
Fall 2017
Due Friday, December 8
1. For the function f (x, y) = x2 + 2xy + 2y 2 + 4x 2y,
(a) Perform one iteration of Newtons method for min
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #6
Fall 2017
Due Friday, October 27
1. For each of the following sets, determine their interior, boundary, and closure.
(a) S1 = cfw_x R : 0 x <
Math-484 Homework #5 (Least squares)
I will nish the homework before 10am Oct 10. If I spot a mathematical mistake I will
let the lecturer know as soon as possible.
I will write clearly and neatly as
Math-484 Homework #1 (warm up)
I will nish the homework before 10am Sep 5. If I spot a mathematical mistake I will let
the lecturer know as soon as possible.
I will write clearly and neatly as the gra
MATH 484 - Exam #3 (sample)
Section . Name: .
Date: Dec 2 2011
Start time . End time: .
Work on your own. Write clearly. Ask if something is not clear. If you need more paper, let me
know. Good luck!
MATH 484 - Exam #2 (sample)
Section . Name: .
Date: Oct 26 2011
Start time 11:00 End time: 11:50
Work on your own. Write clearly. Ask if something is not clear. If you need more paper, let me
know. Go
Math-484 Homework #3 (convex sets and semidenite matrices)
I will nish the homework before 11am Sep 18. If I spot a mathematical mistake I will
let the lecturer know as soon as possible.
I will write
Math-484 Homework #4 (convex functions, (A G) inequality, and some repetition)
I will nish the homework before 11am Sep 25. If I spot a mathematical mistake I will
let the lecturer know as soon as pos
Math-484 Homework #1 (warm up)
I will nish the homework before 11am Sep 4. If I spot a mathematical mistake I will let
the lecturer know as soon as possible.
I will write clearly and neatly as the gra
Math-484 Homework #7 (linear programming)
I will nish the homework before 11am Oct 16. If I spot a mathematical mistake I will
let the lecturer know as soon as possible.
I will write clearly and neatl
Math-484 Homework #6 (Least squares)
I will nish the homework before 10am Oct 17. If I spot a mathematical mistake I will let
the lecturer know as soon as possible.
I will write clearly and neatly as
Math-484 Homework #4 (repetition and (A G) inequality)
I will nish the homework before 10am Sep 26. If I spot a mathematical mistake I will
let the lecturer know as soon as possible.
I will write clea
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #5
Fall 2017
Due Friday, October 13
1. Use the GramSchmidt process to find orthonormal vectors u(1) , u(2) , u(3) R4 that span the
same subspace
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #1
Fall 2017
Due Friday, September 8
1. Find the local and global minimizers of the following functions:
(a) f (x) = x2 + 2x.
2
(b) f (x) = x2 e
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #4
Fall 2017
Due Friday, October 6
1. Consider the geometric program
2
t23
t1
+
: t1 > 0, t2 > 0, t3 > 0 .
min
t2 t3 t1 t2
(a) Find the dual pr
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Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #2
Fall 2017
Due Friday, September 15
1. Using any method you like, classify the matrices below as positive (semi)definite, negative
(semi)defin
Math 484: Nonlinear Programming
Mikhail Lavrov
Homework #3
Fall 2017
Due Friday, September 29
1. Show that the functions are convex on the indicated set.
(a) f (x) = |x3 | on R.
(b) f (x1 , x2 , x3 )