  


On an Extension of Condition Number Theory to NonConic Convex Optimization
Robert M. Freund (rfreundmit.edu) Abstract: The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z_* := min_x {c'x  Axb \in C_Y, x \in C_X }, to the more general nonconic format: (GP_d): z_* := min_x {c'x  Axb \in C_Y, x \in 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 databased 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 conicbased theory of condition numbers to this broader problem format. Keywords: condition number, convex optimization, conic optimization, duality, sensitivity analysis, perturbation theory Category 1: Linear, Cone and Semidefinite Programming Category 2: Linear, Cone and Semidefinite Programming (Other ) Citation: Working paper #200301, USCDepartment of Indstrial and Systems Engineering, Feb/2003 Download: [PDF] Entry Submitted: 02/14/2003 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  