Primal–Dual Interior-Point Methods for Domain-Driven Formulations

Mehdi Karimi () and Levent Tunçel ()
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Mehdi Karimi: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Levent Tunçel: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Mathematics of Operations Research, 2020, vol. 45, issue 2, 591-621

Abstract: We study infeasible-start, primal–dual interior-point methods for convex optimization problems given in a typically natural form we denote as domain-driven formulations. Our algorithms extend many advantages of primal–dual interior-point techniques available for conic formulations, such as the current best complexity bounds, and more robust certificates of approximate optimality, unboundedness, and infeasibility, to domain-driven formulations. The complexity results are new for the infeasible-start setup used even in the case of linear programming. In addition to complexity results, our algorithms aim for expanding the applications of and software for interior-point methods to wider classes of problems beyond optimization over symmetric cones.

Keywords: convex optimization; interior-point methods; primal–dual algorithms; duality theory (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:45:y:2020:i:2:p:591-621

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