Practical Optimization Methods: With Mathematica Applications Book

	Preface
1	Optimization Problem Formulation	1
1.1	Optimization Problem Formulation	2
1.2	The Standard Form of an Optimization Problem	13
1.3	Solution of Optimization Problems	16
1.4	Time Value of Money	18
2	Graphical Optimization	47
2.1	Procedure for Graphical Optimization	48
2.2	Graphical Solution Function	57
2.3	Graphical Optimization Examples	59
3	Mathematical Preliminaries	75
3.1	Vectors and Matrices	75
3.2	Approximation Using the Taylor Series	89
3.3	Solution of Nonlinear Equations	100
3.4	Quadratic Forms	106
3.5	Convex Functions and Convex Optimization Problems	112
4	Optimality Conditions	131
4.1	Optimality Conditions for Unconstrained Problems	132
4.2	The Additive Property of Constraints	144
4.3	Karush-Kuhn-Tucker (KT) Conditions	147
4.4	Geometric Interpretation of KT Conditions	165
4.5	Sensitivity Analysis	175
4.6	Optimality Conditions for Convex Problems	181
4.7	Second-Order Sufficient Conditions	187
4.8	Lagrangian Duality	199
5	Unconstrained Problems	227
5.1	Descent Direction	229
5.2	Line Search Techniques - Step Length Calculations	231
5.3	Unconstrained Minimization Techniques	253
6	Linear Programming	315
6.1	The Standard LP Problem	316
6.2	Solving a Linear System of Equations	319
6.3	Basic Solutions of an LP Problem	334
6.4	The Simplex Method	339
6.5	Unusual Situations Arising During the Simplex Solution	365
6.6	Post-Optimality Analysis	376
6.7	The Revised Simplex Method	387
6.8	Sensitivity Analysis Using the Revised Simplex Method	402
7	Interior Point Methods	437
7.1	Optimality Conditions for Standard LP	438
7.2	The Primal Affine Scaling Method	445
7.3	The Primal-Dual Interior Point Method	464
Appendix	Null and Range Spaces	481
8	Quadratic Programming	495
8.1	KT Conditions for Standard QP	495
8.2	The Primal Affine Scaling Method for Convex QP	502
8.3	The Primal-Dual Method for Convex QP	520
8.4	Active Set Method	535
8.5	Active Set Method for the Dual QP Problem	552
Appendix	Derivation of the Descent Direction Formula for the PAS Method	563
9	Constrained Nonlinear Problems	581
9.1	Normalization	582
9.2	Penalty Methods	585
9.3	Linearization of a Nonlinear Problem	608
9.4	Sequential Linear Programming - SLP	614
9.5	Basic Sequential Quadratic Programming - SQP	620
9.6	Refined SQP Methods	645
Appendix	An Introduction to Mathematica	677
	Bibliography	705
	Index	709