Complexity of convex optimization using geometry-based measures and a reference point
Name
OR-358-01-50876146.pdf
Size
1.41 MB
Format
Adobe PDF
Checksum (MD5)
fc1223daba69e8a291f2b5f53d6e419c
Date Issued
2001
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 358-01
Abstract
Our concern lies in solving the following convex optimization problem: minimize cx subject to Ax=b, x \in P, where P is a closed convex set. We bound the complexity of computing an almost-optimal solution of this problem in terms of natural geometry-based measures of the feasible region and the level-set of almost-optimal solutions, relative to a given reference point xr that might be close to the feasible region and/or the almost-optimal level set. This contrasts with other complexity bounds for convex optimization that rely on data-based condition numbers or algebraic measures, and that do not take into account any a priori reference point information. Keywords: Convex Optimization, Complexity, Interior-Point Method, Barrier Method.
Description
Abstract in HTML and working paper for download in PDF available via World Wide Web at the Social Science Research Network.
Title from cover. "September 2001."
Includes bibliographical references (leaf 29).
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Persistent DSpace Link
