41 citations · 107 across the 13 of their papers we have counts for
9 papers · 1 filter
New complexity bounds for primal--dual interior-point algorithms in conic optimization
Joachim Dahl, Levent Tunçel, Lieven Vandenberghe
We provide improved complexity results for symmetric primal--dual interior-point algorithms in conic optimization. The results follow from new uniform bounds on a key complexity me…
Linear optimization over homogeneous matrix cones
Levent Tunçel, Lieven Vandenberghe
A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a con…
Bregman three-operator splitting methods
Xin Jiang, Lieven Vandenberghe
The paper presents primal-dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update ste…
Regularized Diffusion Adaptation via Conjugate Smoothing
Stefan Vlaski, Lieven Vandenberghe, Ali H. Sayed
The purpose of this work is to develop and study a distributed strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the ex…
Douglas-Rachford splitting for a Lipschitz continuous and a strongly monotone operator
Walaa M. Moursi, Lieven Vandenberghe
The Douglas-Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper closed convex functions; more generally two ma…
Semidefinite representations of gauge functions for structured low-rank matrix decomposition
Hsiao-Han Chao, Lieven Vandenberghe
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which we…
Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems
Martin S. Andersen, Anders Hansson, Lieven Vandenberghe
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality cons…
Decomposition in conic optimization with partially separable structure
Yifan Sun, Martin S. Andersen, Lieven Vandenberghe
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities intro…
Logarithmic barriers for sparse matrix cones
Martin S. Andersen, Joachim Dahl, Lieven Vandenberghe
Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a giv…