On an Extension of Condition Number Theory to Non-Conic Convex Optimization
Name
OR-365-03.pdf
Size
2.06 MB
Format
Adobe PDF
Checksum (MD5)
722ff46a4ebd1817f1987e25639aecf4
Author(s)
Freund, Robert M.
Ordóñez, Fernando, 1970-
Date Issued
February 2003
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 365-03
Abstract
The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z* := minz ctx s.t. Ax - b Cy C Cx , to the more general non-conic format: z* := minx ctx (GPd) s.t. Ax-b E Cy X P, where P is any closed convex set, not necessarily a cone, which we call the groundset. Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory. Herein we extend the modern theory of condition numbers to the problem format (GPd). As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format.
Subjects
Condition number, convex optimization, conic optimization, duality, sensitivity analysis, perturbation theory.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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