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6 papers · 2 filters
Exact Worst-case Performance of First-order Methods for Composite Convex Optimization
Adrien B. Taylor, Julien M. Hendrickx, François Glineur
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimizat…
Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank
Anton Anikin, Alexander Gasnikov, Alexander Gornov +3
In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the…
Complexity of first order inexact Lagrangian and penalty methods for conic convex programming
Ion Necoara, Andrei Patrascu, Francois Glineur
In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or ma…
On the Linear Extension Complexity of Regular n-gons
Arnaud Vandaele, Nicolas Gillis, François Glineur
In this paper, we propose new lower and upper bounds on the linear extension complexity of regular -gons. Our bounds are based on the equivalence between the computation of (i)…
Efficient Method for Computing Lower Bounds on the -radius of Switched Linear Systems
Masaki Ogura, Victor M. Preciado, Raphaël Jungers
This paper proposes lower bounds on a quantity called -norm joint spectral radius, or in short, -radius, of a finite set of matrices. Despite its wide range of applications…
Smooth Strongly Convex Interpolation and Exact Worst-case Performance of First-order Methods
Adrien B. Taylor, Julien M. Hendrickx, François Glineur
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by sol…