Math 164
Fall 2015
Homework 1
Due Friday, Oct 2.
1. Let w = (1, 2, 3)T and b = 5. Find the distance between two planes in R3 dened by
wT x + b = 1
and
2
2
2. Find all values of b such that the matrix
Amanda Nguyen
Department of Economics
UCLA
Economics 103
Introduction to Econometrics
Summer 2013
Problem Set 2 - Due Tuesday July 30
From textbook: (all data sets can be found linked to from the clas
Lecture 1: Optimization Models
Goal:
Mathematical modeling. Standard formulation of optimization problems. Feasible set.
1
Optimization
The general procedure to solve a practical problem
Problem
Mat
Math 164: Optimization
One-Dimensional Search Methods
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
based on Chong-Zak, 4th Ed.
online discussions on piazza.com
Goal of this lectur
Math 164: Optimization
Optimization application examples
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
online discussions on piazza.com
Job assignment problem1
An insurance oce ha
Math 164: Optimization
Support vector machine
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
online discussions on piazza.com
Support vector machine (SVM)
Background: to classify a
Math 164: Introduction to Optimization
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
online discussions on piazza.com
Resource-constrained revenue optimization
m resources; resour
Math 164: Introduction to Optimization
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
online discussions on piazza.com
What is mathematical optimization?
Optimization models the go
Math 164 Homework 3
Lecture 3, 4:00-4:50
Jack Wu
April 21, 2017
Background Material
14.
Since f is convex, f (y+(1)x) = f (x+(yx) f (y)+(1)f (x) f (x+(yx)(1)x f (y).
Thus, f (x + (y x) f (x) + f (x) f
Math 164: Optimization
Gradient Methods
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
some material taken from Chong-Zak, 4th Ed.
online discussions on piazza.com
Main features of
Math 164: Optimization
Conjugate direction methods
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
material taken from the textbook Chong-Zak, 4th Ed., and the CG paper
by Shewchuk
o
Math 164: Optimization
Barzilai-Borwein Method
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
online discussions on piazza.com
Main features of the Barzilai-Borwein (BB) method
The
Math 164: Optimization
Linear programming
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
material taken from the textbook Chong-Zak, 4th Ed.
online discussions on piazza.com
History
Math 164: Optimization
Netwons Method
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
some material taken from Chong-Zak, 4th Ed.
online discussions on piazza.com
Main features of Ne
Math 164: Optimization
Basics of Optimization
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
based on Chong-Zak, 4th Ed.
online discussions on piazza.com
Goals of this lecture
For a
Math 164: Optimization
Nonlinear optimization with inequality constraints
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
material taken from the textbook Chong-Zak, 4th Ed.
online d
Introduction to Optimization
Major subfields
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
online discussions on piazza.com
Overview
Continuous vs Discrete
Continuous optimization:
Math 164: Optimization
Algorithms for constrained optimization
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
material taken from the textbook Chong-Zak, 4th Ed.
online discussions
Math 164: Optimization
Krylov subspace, nonlinear CG, and preconditioning
Instructor: Wotao Yin
Department of Mathematics, UCLA
Spring 2015
material taken from the textbook Chong-Zak, 4th Ed., and the
Math 164 Homework 7
Lecture 3, 4:00-4:50
Jack Wu
May 24, 2017
11.1
a) We Taylor expand f (x(k) + d(k) ) to obtain f (x(k) + d(k) ) = f (x(k) ) + f (x(k) )T d(k) + o(kd(k) )k).
Since f (x(k) )T d(k) <
MATH 164 - Lecture 1 - Summer 2010
Practice Midterm Solutions - July 9, 2010
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Math 164: Optimization
Linear programming
Instructor: Wotao Yin
Department of Mathematics, UCLA
Fall 2017
material taken from the textbook Chong-Zak, 4th Ed.
online discussions on piazza.com
1 / 19
Hi
Math 164: Optimization
Nonlinear optimization with equality constraints
Instructor: Wotao Yin
Department of Mathematics, UCLA
Fall 2017
material taken from the textbook Chong-Zak, 4th Ed.
online discu
Math 164: Optimization
Conjugate direction methods
Instructor: Wotao Yin
Department of Mathematics, UCLA
Fall 2017
material taken from the textbook Chong-Zak, 4th Ed., and the CG paper
by Shewchuk
onl
Math 164: Optimization
The Simplex method
Instructor: Wotao Yin
Department of Mathematics, UCLA
Fall 2017
material taken from the textbook Chong-Zak, 4th Ed.
online discussions on piazza.com
1 / 41
Ov
Math 164: Optimization
Netwons Method
Instructor: Wotao Yin
Department of Mathematics, UCLA
Fall 2017
some material taken from Chong-Zak, 4th Ed.
online discussions on piazza.com
1 / 33
Main features
Optimization
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due November 22, in the discussion section.
Homework 7
Exercise 1. Let E := cfw_(i, j) cfw_1,
Optimization
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due November 29, in the discussion section.
Homework 8
Exercise 1. Let g : [0, 1] R be a cont
Optimization
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due November 1, in the discussion section.
Homework 5
Exercise 1. Is cfw_(x1 , x2 ) R2 : x21
MATH 164, Optimization
Assignment 4
Due: March 5 (Monday). Late homeworks will not be accepted.
1. Consider the least squares problem
minn f (x) := kAx bk2 ,
xR
where A Rmn is NOT necessarily of full
MATH 164, Optimization
Assignment 5
Due: March 16 (Friday). Late homeworks will not be accepted.
1. Consider the linear program
maximize 2x1 + x2
subject to 0 x1 5
0 x2 7
x1 + x2 9.
Convert the probl
MATH 164, Optimization
Assignment 2
Due: Feb 5, Monday. Late homeworks will not be accepted.
1. Consider the problem
min f (x) subject to x ,
where f (x) = 2x1 + 3 and = cfw_x R2 : x21 + x22 1.
(a) F
MATH 164 Optimization
Assignment 1
Due: Monday, Jan 22. Late homeworks will not be accepted.
n
1. Let cfw_xk
k=1 R be a convergent sequence, prove that there exists B > 0 such
that kxk k B for all k