'I recommend this book to anyone desiring a deep understanding of the simplex method, interior-point methods, and the connections between them.' Interfaces, 27:2 (1997) The book is clearly written. ... It is highly recommended to anybody wishing to get a clear insight in the field and in the role that duality plays not only from a theoretical point of view but also in connection with algorithms.' Optimization, 40 (1997)

• 1 Introduction.- 1.1 The Problem.- 1.2 Prototype Problems.- 1.3 About this Book.- 1.4 Notes.- 2 Background.- 2.1 Real Analysis.- 2.2 Linear Algebra and Matrix Analysis.- 2.3 Numerical Linear Algebra.- 2.4 Convexity and Separation Theorems.- 2.5 Linear Equations and Inequalities.- 2.6 Convex Polyhedral Sets.- 2.7 Nonlinear System of Equations.- 2.8 Notes.- 3 Duality Theory and Optimality Conditions.- 3.1 The Dual Problem.- 3.2 Duality Theorems.- 3.3 Optimality and Complementary Slackness.- 3.4 Complementary Pair of Variables.- 3.5 Degeneracy and Uniqueness.- 3.6 Notes.- 4 Boundary Methods.- 4.1 Introduction.- 4.2 Primal Simplex Method.- 4.3 Bounded Variable Simplex Method.- 4.4 Dual Simplex Method.- 4.5 Primal — Dual Method.- 4.6 Notes.- 5 Interior Point Methods.- 5.1 Primal Affine Scaling Method.- 5.2 Degeneracy Resolution by Step-Size Control.- 5.3 Accelerated Affine Scaling Method.- 5.4 Primal Power Affine Scaling Method.- 5.5 Obtaining an Initial Interior Point.- 5.6 Bounded Variable Affine Scaling Method.- 5.7 Affine Scaling and Unrestricted Variables.- 5.8 Dual Affine Scaling Method.- 5.9 Primal-Dual Affine Scaling Method.- 5.10 Path Following or Homotopy Methods.- 5.11 Projective Transformation Method.- 5.12 Method and Unrestricted Variables.- 5.13 Notes.- 6 Implementation.- 6.1 Implementation of Boundary Methods.- 6.2 Implementation of Interior Point Methods.- 6.3 Notes.- A Tables.

'I recommend this book to anyone desiring a deep understanding of the simplex method, interior-point methods, and the connections between them.' Interfaces, 27:2 (1997) The book is clearly written. ... It is highly recommended to anybody wishing to get a clear insight in the field and in the role that duality plays not only from a theoretical point of view but also in connection with algorithms.' Optimization, 40 (1997)

• 1 Introduction.- 1.1 The Problem.- 1.2 Prototype Problems.- 1.3 About this Book.- 1.4 Notes.- 2 Background.- 2.1 Real Analysis.- 2.2 Linear Algebra and Matrix Analysis.- 2.3 Numerical Linear Algebra.- 2.4 Convexity and Separation Theorems.- 2.5 Linear Equations and Inequalities.- 2.6 Convex Polyhedral Sets.- 2.7 Nonlinear System of Equations.- 2.8 Notes.- 3 Duality Theory and Optimality Conditions.- 3.1 The Dual Problem.- 3.2 Duality Theorems.- 3.3 Optimality and Complementary Slackness.- 3.4 Complementary Pair of Variables.- 3.5 Degeneracy and Uniqueness.- 3.6 Notes.- 4 Boundary Methods.- 4.1 Introduction.- 4.2 Primal Simplex Method.- 4.3 Bounded Variable Simplex Method.- 4.4 Dual Simplex Method.- 4.5 Primal — Dual Method.- 4.6 Notes.- 5 Interior Point Methods.- 5.1 Primal Affine Scaling Method.- 5.2 Degeneracy Resolution by Step-Size Control.- 5.3 Accelerated Affine Scaling Method.- 5.4 Primal Power Affine Scaling Method.- 5.5 Obtaining an Initial Interior Point.- 5.6 Bounded Variable Affine Scaling Method.- 5.7 Affine Scaling and Unrestricted Variables.- 5.8 Dual Affine Scaling Method.- 5.9 Primal-Dual Affine Scaling Method.- 5.10 Path Following or Homotopy Methods.- 5.11 Projective Transformation Method.- 5.12 Method and Unrestricted Variables.- 5.13 Notes.- 6 Implementation.- 6.1 Implementation of Boundary Methods.- 6.2 Implementation of Interior Point Methods.- 6.3 Notes.- A Tables.