Interior Point Methods for Linear Optimization

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.