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A Mathematical View of Interior-point Methods for Convex Optimization (2001)
| Venue: | IN CONVEX OPTIMIZATION, MPS/SIAM SERIES ON OPTIMIZATION, SIAM |
| Citations: | 267 - 2 self |
BibTeX
@INPROCEEDINGS{Renegar01amathematical,
author = {James Renegar},
title = {A Mathematical View of Interior-point Methods for Convex Optimization },
booktitle = {IN CONVEX OPTIMIZATION, MPS/SIAM SERIES ON OPTIMIZATION, SIAM},
year = {2001},
publisher = {}
}
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Abstract
These lecture notes aim at developing a thorough understanding of the core theory for interior-point methods. The overall theory continues to grow ata rapid rate but the core ideas have remained largely unchanged for several years, since Nesterov and Nemirovskii [1] published their path-breaking, broadly-encompassing and enormously influential work. Since then, what has changed about the core ideas is our conception of them. Whereas [1] is notoriously difficult reading even for specialists, we now know how to motivate and present the general theory in such away as to make it accessible for non-specialists and PhD students. Therein lies the justification for these lecture notes. We develop the theory in R^n although most of the theory can be developed in arbitrary real Hilbert spaces. The restriction to finite dimensions is primarily for accessibility. The notes were developed largely in conjunction with a PhD-level course on interior-point methods at Cornell University.
