Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms

By Jiming Peng; Cornelis Roos et al. | Go to book overview

Chapter 1
Introduction and Preliminaries

Linear Programming is a revolutionary development that permits us, for the first time in our long evolutionary history, to make decisions about the complex world in which we live that can approximate, in some sense, the optimal or best decision.

George B. Dantzig [80]

A short survey about the fields of linear optimization1 and interior-point methods is presented in this chapter. Based on the simple model of standard linear optimization problems, some basic concepts of interior-point methods and various strategies used in the algorithm are introduced. The purpose of this work, as well as some intuitive observations that sparked the authors' research, are described. Several preliminary technical results are presented as a preparation for later analysis, and the contents of the book are also outlined.

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1
For some historical reason, the name “linear programming” was coined in the early stages of the field of linear optimization. In this monograph we choose its more natural name “linear optimization”. This also distinguishes the field from general programming works related to computers.

-1-

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