16 Unconstrained Optimization Chap. 1
_ 5 W
(2+ ng )d2'
It is seen that Eq. (1.4) is satised for any 6 > 0 and 7 > 0 such that
A 0(lldH2) Y .
_ > - .
2+ lldllg _ 2, Vd With |dH<e
Q.E.D.
E X E R C I S E S
1.1.].
For each value of the scalar ,8, nd the
File List:
The Matlab files are oriented in the following order:
assignment2.m This is the main file for running all the programming problems. The problem size and
condition number can be modified from this file.
armijo_quad.m This file contains code for
Recitation 1 Solutions
February 20, 2005
1.1.9
For any x, y Rn , from the second order expansion (see Appendix A, Proposition A.23)
we have
1
f (y) f (x) = (y x) f (x) + (y x) 2 f (z)(y x),
(1)
2
where z is some point of the line segment joining x and y.
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
luozq@ece.umn.edu
Lecture 8: Constrained Optimization: Duality Theory
Convex Cost/Linear Constraints
Duality Theor
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
luozq@ece.umn.edu
Lecture 4: Optimal First Order Methods
Unconstrained smooth convex minimization
Analysis of clas
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
luozq@ece.umn.edu
Lecture 1
Zhi-Quan Luo
Lecture 1 Unconstrained Optimization
Denitions
Necessary rst/second order
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
luozq@ece.umn.edu
Lecture 2
Zhi-Quan Luo
Lecture 2: Gradient Methods
Gradient Methods - Motivation
Principal Gradi
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
luozq@ece.umn.edu
Lecture 0
Zhi-Quan Luo
Organization
Instructor:
Dr. Tom Luo (luozq@ece.umn.edu),
Dept. Electrical
Fall 2016 EE 5239: Introduction to Nonlinear Optimization
Homework Set 4
Due by 4:00pm, Monday October 24
1. Exercise 2.1.6 in the textbook
2. Exercise 2.1.7 in the textbook
3. Exercise 2.3.1 in the textbook
4. Exercise 3.1.3 in the textbook
1
EE 5239: Introduction to Nonlinear Optimization
Homework Set 3
Due date: 4:00pm, Wednesday October 12, 2016
1. Exercise 1.4.1 in the textbook
2. Exercise 1.4.8 in the textbook
3. Exercise 1.4.9 in the textbook
4. Exercise 1.5.1 in the textbook
5. Exercise
Nonlinear Programming
3rd Edition
Theoretical Solutions Manual
Chapter 1
Dimitri P. Bertsekas
Massachusetts Institute of Technology
Athena Scientific, Belmont, Massachusetts
1
NOTE
This manual contains solutions of the theoretical problems, marked in the
16 Unconstrained Optimization Chap. 1
_ 5 W
(2+ ng )d2'
It is seen that Eq. (1.4) is satised for any 6 > 0 and 7 > 0 such that
A 0(lldH2) Y .
_ > - .
2+ lldllg _ 2, Vd With |dH<e
Q.E.D.
E X E R C I S E S
1.1.].
For each value of the scalar ,8, nd the
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
luozq@ece.umn.edu
Lecture 4: Optimal First Order Methods
Unconstrained smooth convex minimization
Analysis of clas
EE 5239: Introduction to Nonlinear Optimization
Homework Set 2
Due date: 4:00pm, Monday October 3, 2016
1. Exercise 1.2.1 in the textbook
2. Exercise 1.2.2 in the textbook
3. Exercise 1.2.3 in the textbook
4. Exercise 1.2.6 in the textbook
5. Exercise 1.2
Solutions to Homework 1
February 24, 2010
1. Bertsekas 1.1.1: Given the function
f (x, y) = x2 + y 2 + xy + x + 2y,
we need to determine which of its stationary points are minima. From the set of necessary conditions f = 0,
we get
2x + y
x + 2y
= 1
= 2.
W