Advisor

Prof. Sebastian Pokutta, Institute of Mathematics, Technische Universität Berlin and Department for AI in Society, Science, and Technology, Zuse Institute Berlin (Advisor)

Committee

1. Prof. Alexandre d'Aspremont, Département d'Informatique, CNRS and École Normale Supérieure

2. Prof. Jelena Diakonikolas, Department of Computer Science, University of Wisconsin–Madison

3. Prof. Swati Gupta, School of Industrial and Systems Engineering, Georgia Institute of Technology

4. Prof. Guanghui Lan, School of Industrial and Systems Engineering, Georgia Institute of Technology

Abstract

In this thesis, we focus on Frank-Wolfe (a.k.a. Conditional Gradient) algorithms, a family of iterative algorithms for convex optimization, that work under the assumption that projections onto the feasible region are prohibitive, but linear optimization problems can be efficiently solved over the feasible region. We present several algorithms that either locally or globally improve upon existing convergence guarantees. In Chapters 2-4 we focus on the case where the objective function is smooth and strongly convex and the feasible region is a polytope, and in Chapter 5 we focus on the case where the function is generalized self-concordant and the feasible region is a compact convex set.