Status Determination by Interior-Point Methods for Convex Optimization Problems in Domain-Driven Form
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.
Cite
@article{arxiv.1901.07084,
title = {Status Determination by Interior-Point Methods for Convex Optimization Problems in Domain-Driven Form},
author = {Mehdi Karimi and Levent Tunçel},
journal= {arXiv preprint arXiv:1901.07084},
year = {2019}
}