- On an Extension of Condition Number Theory to Non-Conic Convex Optimization Robert M. Freund (rfreundmit.edu) Fernando Ordonez (fordonusc.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 | Ax-b \in C_Y, x \in C_X }, to the more general non-conic format: (GP_d): z_* := min_x {c'x | Ax-b \in C_Y, x \in P}, 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. 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 #2003-01, USC-Department of Indstrial and Systems Engineering, Feb/2003 Download: [PDF]Entry Submitted: 02/14/2003Entry Accepted: 02/14/2003Entry Last Modified: 02/14/2003Modify/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 Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.