Introduction to global optimization
Global optimization problems are extraordinarily di verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering.
Print Book, English, ©2000
Kluwer Academic Publishers, Dordrecht, ©2000
xiv, 353 pages : illustrations ; 25 cm.
9780792365747, 9780792367567, 0792365747, 0792367561
44712904
1. Fundamental Results
Convex Sets and Functions
General Properties of Optimization Problems
Convex Envelops
Kuhn-Tucker Conditions
Second Order Optimality Conditions
Duality in Nonlinear Programming
Complexity Issues
2. Quadratic Programming
Quadratic Integer Programming
Linear Complementarity Problem
Complexity of Quadratic Optimization
Enumerative Methods
Separation and Interpolation
3. General Concave Minimization
Applications
Basic Operations
Cutting Plane Algorithms
Outer Approximation Algorithms
Inner Approximation
Branch and Bound Algorithms
A Simplicial Branch and Bound Approach
4. D.C. Programming
The Space of D.C. Functions
Some Additional Applications
Optimality Conditions
The Canonical D.C. Program
A Simplicial Branch and Bound Algorithm
A Prismatic Algorithm
5. Lipschitz Optimization
Lipschitz Functions
Lipschitz Optimization Problems
Lower Bounds
Branch and Bound Algorithms
Implementation
6. Global Optimization on Networks
Some MCCFP Models and its Complexity
Solution Methods
7. Decomposition Algorithms
Variable Decomposition: Conical Algorithm
Variable Decomposition: Outer Approximation
Constraint Decomposition: Conical Algorithm
Constraint Decomposition: Cutting Algorithm