On an extension of condition number theory to nonconic convex optimization

• 成果类型: Article
• 署名作者: Freund, RM; Ordónez, F
• 署名单位: Massachusetts Institute of Technology (MIT); University of Southern California
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1040.0120
• 发表日期: 2005
• 页码: 173-194
• 关键词: ill-posedness; complexity; systems

摘要

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: [GRAPHICS] to the more general nonconic format: [GRAPHICS] where P is any closed convex set, not necessarily a cone, which we call the ground-set. 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 (GP(d)). 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.