Optimization Online


Status Determination by Interior-Point Methods for Convex Optimization Problems in Domain-Driven Form

Mehdi Karimi(m7karimi***at***uwaterloo.ca)
Levent Tuncel(ltuncel***at***math.uwaterloo.ca)

Abstract: We study the geometry of convex optimization problems given in a Domain-Driven form and categorize possible statuses of these problems using duality theory. Our duality theory for the Domain-Driven form, which accepts both conic and non-conic constraints, lets us determine and certify statuses of a problem as rigorously as the best approaches for conic formulations (which have been demonstrably very efficient in this context). We analyze the performance of an infeasible-start primal-dual algorithm for the Domain-Driven form in returning the certificates for the defined statuses. Our iteration complexity bounds for this more practical Domain-Driven form match the best ones available for conic formulations. At the end, we propose some stopping criteria for practical algorithms based on insights gained from our analyses.

Keywords: convex optimization, interior-point methods, primal-dual algorithms, duality theory, status determination

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Department of Combinatorics and Optimization, University of Waterloo,

Download: [PDF]

Entry Submitted: 02/28/2019
Entry Accepted: 02/28/2019
Entry Last Modified: 02/28/2019

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society