Fundamental Engineering Optimization Methods

Cover......Page 1
Fundamental Engineering Optimization Methods......Page 2
©......Page 3
Contents......Page 4
Preface......Page 8
1.1	Introduction......Page 10
1.2	Optimization Examples in Science and Engineering......Page 11
1.3	Notation......Page 18
2.1	Set Definitions......Page 19
2.2	Function Definitions......Page 20
2.3	Taylor Series Approximation......Page 21
2.4	Gradient Vector and Hessian Matrix......Page 23
2.5	Convex Optimization Problems......Page 24
2.7	Matrix Eigenvalues and Singular Values......Page 26
2.8	Quadratic Function Forms......Page 27
2.9	Linear Systems of Equations......Page 28
2.11	Condition Number and Convergence Rates......Page 30
2.12	 Conjugate-Gradient Method for Linear Equations......Page 32
2.13	Newton’s Method for Nonlinear Equations......Page 33
3	Graphical Optimization......Page 34
3.1	Functional Minimization in One-Dimension......Page 35
3.2	Graphical Optimization in Two-Dimensions......Page 36
4	Mathematical Optimization......Page 43
4.1	The Optimization Problem......Page 44
4.2	Optimality criteria for the Unconstrained Problems......Page 45
4.3	Optimality Criteria for the Constrained Problems......Page 48
4.4	Optimality Criteria for General Optimization Problems......Page 54
4.5	Postoptimality Analysis......Page 59
4.6	Lagrangian Duality......Page 60
5.1	The Standard LP Problem......Page 68
5.2	The Basic Solution to the LP Problem......Page 70
5.3	The Simplex Method......Page 72
5.4	Postoptimality Analysis......Page 84
5.5	Duality Theory for the LP Problems......Page 89
5.6	Non-Simplex Methods for Solving LP Problems......Page 97
5.7	Optimality Conditions for LP Problems......Page 101
5.8	The Quadratic Programming Problem......Page 104
5.9	The Linear Complementary Problem......Page 108
6.1	Discrete Optimization Problems......Page 113
6.2	Solution Approaches to Discrete Problems......Page 114
6.3	Linear Programming Problems with Integral Coefficients......Page 115
6.5	Integer Programming Problems......Page 119
7	Numerical Optimization Methods......Page 126
7.1	The Iterative Method......Page 127
7.2	Computer Methods for Solving the Line Search Problem......Page 128
7.3	Computer Methods for Finding the Search Direction......Page 134
7.4	Computer Methods for Solving the Constrained Problems......Page 146
7.5	Sequential Linear Programming......Page 151
7.6	Sequential Quadratic Programming......Page 153
8	References......Page 162