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Lecture Notes on Nonlinear Optimization
Jane J. Ye, University of Victoria
August 25, 2015
2
Contents
1 Mathematical Preliminaries
1.1 Functions of several variables
1.2 Review of differentiation . . .
1.3 Review of matrix theory . . .
1.4 The implicit fu
Chapter 1:
Vectors and Coordinate Geometry in 3-Space
Week 1-2: Algebra and Geometry of Vectors
I. Rectangular Coordinates
z
y
(2,2,3)
(2,3)
3
y
2
x
2
x
Rectangular coordinate system
Righthanded rectangular
for 2space
coordinate system for 3space
Geometry
Chapter 2: Vector Functions and Curves
I. Calculus of Vector-valued Functions
A vector parametric equation of a line in 2-space
(plane), or 3-space, looks like:
~r = ~a + t~v,
< t <
Considering it as a time-dependent vector,
~r = ~r(t) = ~a + t~v
we hav
Math 2215 Mathematical Analysis, Tutorial 3 (Feb 01, 2016)
How to define being close to each other?
Neighborhood (Notation: N (x, )
Given x R and > 0 , N (x, ) = cfw_y : |x y| < e.
- Neighborhood is a set collecting all y which is -close to x.
- Use neig
Linear Programming and Integer Programming
Assignment 1
October 4, 2016
(Submit on or before the class of October 17, 2016, Monday)
The first Mid-term exam will be on October 17, 2016, Monday
1. Solve the following problem by showing the simplex tableau a
Chapter 4
Duality Theory and Sensitivity Analysis
Also see Chapter 6 of the text book.
One of the most important discoveries in the early development of linear programming
was the concept of duality and its many important ramifications. This discovery rev
Chapter 3
The Theory of the Simplex Method
Also see Chapter 5 of the text book.
Chapter 2 introduced the basic mechanics of the simplex method. Now we shall delve
a little more deeply into this algorithm by examining some of its underlying theory. The
fir
Hong Kong Baptist University
Faculty of Science
Department of Mathematics
Title (Units):
MATH 3205 Linear and Integer Programming (3,3,0)
Course Aims:
This course aims to introduce students to the fundamental topics in
Linear and Integer programming. Stud
Linear Programming and Integer Programming
Mid-term Examination
Solution
1.
(a) True. Hint: Recall the definitions of polyhedra set and convexity.
(b) False. Hint: Let the obj equal 0. Then every BFS is optimal, and in general every BFS is clearly not
adj
MATH 2207: Linear Algebra, Autumn 2015
Course
Information
Lecture Time and Venue: WED 15:3017:20 @ AAB204
THU 11:3012:20 @ LT1
Homepage: http:/www.math.hkbu.edu.hk/felix kwok/math2207/
Instructor
Information
Name: Dr. Felix KWOK
Office: FSC1103
Phone: (85
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