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Primal-Dual Interior-Point Methods for Domain-Driven Formulations: Algorithms

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

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 formulation. 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, self-concordant barriers

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 04/18/2018
Entry Accepted: 04/19/2018
Entry Last Modified: 04/18/2018

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