Undergraduate Convexity: Problems And Solutions

by Mikkel Slot Nielsen, Victor Ulrich Rohde

Overview

This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here

Product Details

ISBN-13:	9789813146211
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	11/08/2016
Pages:	196
Product dimensions:	6.10(w) x 9.00(h) x 0.70(d)

Table of Contents

Preface v

Acknowledgments vii

1 Fourier-Motzkin elimination 1

1.1 Introduction 1

1.2 Exercises and solutions 2

2 Affine subspaces 13

2.1 Introduction 13

2.2 Exercises and solutions 14

3 Convex subsets 23

3.1 Introduction 23

3.2 Exercises and solutions 24

4 Polyhedra 49

4.1 Introduction 49

4.2 Exercises and solutions 61

5 Computations with polyhedra 61

5.1 Introduction 61

5.2 Exercises and solutions 62

6 Closed convex subsets and separating hyperplanes 81

6.1 Introduction 81

6.2 Exercises and solutions 82

7 Convex functions 99

7.1 Introduction 99

7.2 Exercises and solutions 101

8 Differentiable functions of several variables 113

5.1 Introduction 113

8.1 Exercises and solutions 114

9 Convex functions of several variables 123

9.1 Introduction 123

9.2 Exercises and solutions 125

10 Convex optimization 147

10.1 Introduction 147

10.2 Exercises and solutions 149

Appendix A Analysis 175

A.1 Introduction 175

A.2 Exercises and solutions 176

Appendix B Linear (in)dependence and the rank of a matrix 181

B.1 Introduction 181

B.2 Exercises and solutions 182