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Status Determination by Interior-Point Methods for Convex Optimization Problems in Domain-Driven Form
Mehdi Karimi(m7karimi 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 Modify/Update this entry | ||
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