Table of Contents

Chapter 1: Introduction 1

1.1, 1.2, 1.4, 1.6, 1.10, 1.13

Chapter 2 Convex Sets 4

2.1, 2.2, 2.3, 2.7, 2.8, 2.12, 2.15, 2.21, 2.24, 2.31, 2.42, 2.45, 2.47, 2.49, 2.50, 2.51, 2.52, 2.53, 2.57

Chapter 3: Convex Functions and Generalizations 15

3.1, 3.2, 3.3, 3.4, 3.9, 3,10, 3.11, 3.16, 3.18, 3.21, 3.22, 3.26, 3.27, 3.28, 3.31, 3.37, 3.39, 3.40, 3.41, 3.45, 3.48, 3.51, 3.54, 3.56, 3.61, 3.62, 3.63, 3.64, 3.65

Chapter 4: The Fritz John and Karush-Kuhn-Tucker Optimality Conditions 29

4.1, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.12, 4.15, 4.27, 4.28, 4.30, 4.31, 4.33, 4.37, 4.41, 4.43

Chapter 5: Constraint Qualifications 46

5.1, 5.12, 5.13, 5.15, 5.20

Chapter 6: Lagrangian Duality and Saddle Point Optimality Conditions 51

6.2, 6.3, 6.4, 6.5, 6.7, 6.8, 6.9, 6.14, 6.15, 6.21, 6.23, 6.27, 6.29,

Chapter 7: The Concept of an Algorithm 64

7.1, 7.2, 7.3, 7.6, 7.7, 7.19

Chapter 8: Unconstrained Optimization 69

8.10, 8.11, 8.12, 8.18, 8.19, 8.21, 8.23, 8.27, 8.28, 8.32, 8.35, 8.41, 8.47, 8.51, 8.52

Chapter 9: Penalty and Barrier Functions 88

9.2, 9.7, 9.8, 9.12, 9.13, 9.14, 9.16, 9.19, 9.32

Chapter 10: Methods of Feasible Directions 107

10.3, 10.4, 10.9, 1.012, 10.19, 10.20, 10.25, 10.33, 10.36, 10.41, 10.44, 10.47, 10.52

Chapter 11: Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programing 134

11.1, 11.5, 11.12, 11.18, 11.19, 11.22, 11.23, 11.24, 11.36, 11.41, 11.42, 11.47, 11.48, 11.50, 11.51, 11.52

About the Author

Mokhtar S. Bazaraa and C.M. Shetty are Professors Emeriti at Georgia Institute of Technology. Hanif D. Sherali, the lead author, is a W. Thomas Rice Chaired Professor of Engineering in the Grado Department of Industrial and Systems Engineering at the Virginia Polytechnic and State University. He and Dr. Bazaraa are co-authors of a complementary best-selling book at Wiley on linear programming (LP). Solutions prepared by Joanna Leleno.