PART I MATHEMATICAL REVIEW 1 Methods of Proof and Some Notation 3 2 Vector Spaces and Matrices 7 3 Transformations 25 4 Concepts from Geometry 45 5 Elements of Calculus 55
PART II UNCONSTRAINED OPTIMIZATION 6 Basics of Set-Constrained and Unconstrained Optimization 81 7 One-Dimensional Search Methods 103 8 Gradient Methods 131 9 Newton¡¯s Method 161 10 Conjugate Direction Methods 175 11 Quasi-Newton Methods 193 12 Solving Linear Equations 217 13 Unconstrained Optimization and Neural Networks 253 14 Global Search Algorithms 273 PART III LINEAR PROGRAMMING 15 Introduction to Linear Programming 305 16 Simplex Method 339 17 Duality 379 18 Nonsimplex Methods 403 19 Integer Linear Programming 429 PART IV NONLINEAR CONSTRAINED OPTIMIZATION 20 Problems with Equality Constraints 453 21 Problems with Inequality Constraints 487 22 Convex Optimization Problems 509 23 Algorithms for Constrained Optimization 549 24 Multiobjective Optimization 577 |