Optimization Theory

• Main Authors: Jongen, Hubertus Th (Author), Meer, Klaus (Author), Triesch, Eberhard (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2004.
• Subjects: Mathematics.; Computers.; Computer science > Mathematics.; Mathematical optimization.; Optimization.; Discrete Mathematics in Computer Science.; Theory of Computation.

Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc. This volume gives a comprehensive introduction into...

Table of Contents:

• Optimality Criteria on Simple Regions
• Constraints, Lagrange Function, Optimality Criteria
• Parametric Aspects, Semi-Infinite Optimization
• Convex Functions, Duality, Separation Theorem
• Linear Inequalities, Constraint Qualifications
• Linear Programming: The Simplex Method
• The Ellipsoid Method
• The Method of Karmarkar for Linear Programming
• Order of Convergence, Steepest Descent, (Lagrange -)Newton
• Conjugate Direction, Variable Metric
• Penalty-, Barrier-, Multiplier-, Interior Point-Methods
• Search Methods without Derivatives
• One-Dimensional Minimization
• Graphs and Networks
• Flows in Networks
• Applications of the Max-Flow Min-Cut Theorem
• Integer Linear Programming
• Computability; the Turing machine
• Complexity theory
• Reducibility and NP-completeness
• Some NP-completeness results
• The Random Access Machine
• Complexity Theory over the Real Numbers
• Approximating NP-hard Problems
• Approximation Algorithms for TSP
• Approximation algorithms for Bin Packing
• A FPTAS for Knapsack
• Miscellaneous.