Interior Point Methods for Linear Optimization

• Main Authors: Roos, Cornelis (Author), Terlaky, Tamás (Author), Vial, Jean-Philiipe (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2005.
• Edition: Revised Edition.
• Subjects: Mathematics.; Algorithms.; Computer mathematics.; Mathematical optimization.; Operations research.; Management science.; Optimization.; Operations Research, Management Science.; Computational Science and Engineering.

Linear Optimization (LO) is one of the most widely applied and taught techniques in mathematics, with applications in many areas of science, commerce and industry. The dramatically increased interest in the subject is due mainly to advances in computer technology and the development of Interior Poin...

Table of Contents:

• Introduction: Theory and Complexity
• Duality Theory for Linear Optimization
• A Polynomial Algorithm for the Self—dual Model
• Solving the Canonical Problem
• The Logarithmic Barrier Approach
• Preliminaries
• The Dual Logarithmic Barrier Method
• The Primal—Dual Logarithmic Barrier Method
• Initialization
• The Target-following Approach
• Preliminaries
• The Primal-Dual Newton Method
• Applications
• The Dual Newton Method
• The Primal Newton Method
• Application to the Method of Centers
• Miscellaneous Topics
• Karmarkar’s Projective Method
• More Properties of the Central Path
• Partial Updating
• Higher-Order Methods
• Parametric and Sensitivity Analysis
• Implementing Interior Point Methods.