Cover -- Title Page -- Contents -- Preface -- Table of Notation -- PART 1 UNCONSTRAINED OPTIMIZATION -- Chapter 1 Introduction -- 1.1 History and Applications -- 1.2 Mathematical Background -- Questions for Chapter 1 -- Chapter 2 Structure of Methods -- 2.1 Conditions for Local Minima -- 2.2 Ad hoc Methods -- 2.3 Useful Algorithmic Properties -- 2.4 Quadratic Models -- 2.5 Descent Methods and Stability -- 2.6 Algorithms for the Line Search Subproblem -- Questions for Chapter 2 -- Chapter 3 Newton-like Methods -- 3.1 Newton's Method -- 3.2 Quasi-Newton Methods -- 3.3 Invariance -- 3.4 The Broyden Family -- 3.5 Numerical Experiments -- 3.6 Other Formulae -- Questions for Chapter 3 -- Chapter 4 Conjugate Direction Methods -- 4.1 Conjugate Gradient Methods -- 4.2 Direction Set Methods -- Questions for Chapter 4 -- Chapter 5 Restricted Step Methods -- 5.1 A Prototype Algorithm -- 5.2 Levenberg-Marquardt Methods -- Questions for Chapter 5 -- Chapter 6 Sums of Squares and Nonlinear Equations -- 6.1 Over-determined Systems -- 6.2 Well-determined Systems -- 6.3 No-derivative Methods -- Questions for Chapter 6 -- PART 2 CONSTRAINED OPTIMIZATION -- Chapter 7 Introduction -- 7.1 Preview -- 7.2 Elimination and Other Transformations -- Questions for Chapter 7 -- Chapter 8 Linear Programming -- 8.1 Structure -- 8.2 The Simplex Method -- 8.3 Other LP Techniques -- 8.4 Feasible Points for Linear Constraints -- 8.5 Stable and Large-scale Linear Programming -- 8.6 Degeneracy -- 8.7 Polynomial Time Algorithms -- Questions for Chapter 8 -- Chapter 9 The Theory of Constrained Optimization -- 9.1 Lagrange Multipliers -- 9.2 First Order Conditions -- 9.3 Second Order Conditions -- 9.4 Convexity -- 9.5 Duality -- Questions for Chapter 9 -- Chapter 10 Quadratic Programming -- 10.1 Equality Constraints -- 10.2 Lagrangian Methods.

10.3 Active Set Methods -- 10.4 Advanced Features -- 10.5 Special QP Problems -- 10.6 Complementary Pivoting and Other Methods -- Questions for Chapter 10 -- Chapter 11 General Linearly Constrained Optimization -- 11.1 Equality Constraints -- 11.2 Inequality Constraints -- 11.3 Zigzagging -- Questions for Chapter 11 -- Chapter 12 Nonlinear Programming -- 12.1 Penalty and Barrier Functions -- 12.2 Multiplier Penalty Functions -- 12.3 The L1 Exact Penalty Function -- 12.4 The Lagrange-Newton Method (SQP) -- 12.5 Nonlinear Elimination and Feasible Direction Methods ... -- 12.6 Other Methods -- Questions for Chapter 12 -- Chapter 13 Other Optimization Problems -- 13.1 Integer Programming -- 13.2 Geometric Programming -- 13.3 Network Programming -- Questions for Chapter 13 -- Chapter 14 Non-Smooth Optimization -- 14.1 Introduction -- 14.2 Optimally Conditions -- 14.3 Exact Penalty Functions -- 14.4 Algorithms -- 14.5 A Globally Convergent Prototype Algorithm -- 14.6 Constrained Non-Smooth Optimization -- Questions for Chapter 14 -- References -- Subject Index.