Math 432/532
Homework
20 pts.
Due Feb. 3, 2012
1. For the following functions, all critical points are listed. Identify all local and global maxima and minima, along with saddle points. (a) f (x, y) =
Math 432/532
Spring 2012
Announcement of March 14 test
Our second test will be on Wednesday, March 14. It will cover the material from our last three homework assignments. The main topics are these: T
Math 432/532
Homework
15 points
Due March 23, 2012
1. Let f (x1 , x2 ) = 2x1 4 + x2 2 - 4x1 x2 + 5x2 . (a) Compute the first two terms x(1) , x(2) of the Newton's method sequence for finding a critica
Math 432/532
Homework
15 points
Due March 2, 2012
1. Find the equation of the line that gives the best "least-squares fit" to the data points (-2, 12), (-1, 11), (0, 8), (1, 5), (2, 2), (3, -3). 2. Fi
Math 432/532
Homework
15 points
Due February 17, 2012
1. Which of the following functions are convex on the specified convex sets? Which are strictly convex? (a) f (x1 , x2 ) = 5x1 2 + x2 2 + 2x1 x2 -
Math 432/532
Homework
15 pts.
Due January 20, 2012
432 students: Solve any 5 of the 6 problems. 532 students: Solve all 6 problems. 1. Find the local and global minimizers and maximizers of the follow
8. LINEAR PROGRAMMING
Linear programming is the most widely used class of constrained optimization problems. Its special structure provides for strong theoretical results and efficient algorithms.
8.1
7. GENERAL NONLINEAR PROGRAMMING
In this chapter we develop necessary and sufficient conditions for optimality for the general nonlinear programming problem (NLP) minimize f (x) subject to gi (x) = 0,
6. LINEAR LEAST SQUARES AND RELATED PROBLEMS
Linear least squares constitutes one of the most important classes of optimization problems in modern society, primarily because of its central role in sta
5. ITERATIVE METHODS FOR OPTIMIZATION
Our first step in solving an optimization problem is to use some form of necessary condition to identify candidates for optimality. For unconstrained problems, th
4. CONVEXITY AND OPTIMIZATION
Convexity plays a natural role in optimization. It has tremendous intuitive appeal and provides powerful and elegant approaches to a wide variety of pure and applied prob
3. EXISTENCE OF GLOBAL OPTIMIZERS
This chapter presents theoretical tools for demonstrating the existence of global minimizers or maximizers. For practical purposes, such tools enable us to verify glo
2. UNCONSTRAINED OPTIMIZATION
In this chapter, we develop principles for identifying and validating candidates for optimality in problems with no explicit constraints: min f (x) over all x S, where S
MTH 432/532 LECTURE NOTES Spring 2009
INTRODUCTION TO LINEAR AND NONLINEAR PROGRAMMING
S. Wright
Department of Mathematics & Statistics Miami University, Oxford, OH
c 2008, 2009
Table of Contents
1. I