Lieven Vandenberghe
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View article: New complexity bounds for primal--dual interior-point algorithms in conic optimization
New complexity bounds for primal--dual interior-point algorithms in conic optimization Open
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 measure for primal--dual metrics at pairs of primal and dual …
View article: Minimum-rank positive semidefinite matrix completion with chordal patterns and applications to semidefinite relaxations
Minimum-rank positive semidefinite matrix completion with chordal patterns and applications to semidefinite relaxations Open
We present an algorithm for computing the minimum-rank positive semidefinite completion of a sparse matrix with a chordal sparsity pattern. This problem is tractable, in contrast to the minimum-rank positive semidefinite completion problem…
View article: Linear optimization over homogeneous matrix cones
Linear optimization over homogeneous matrix cones Open
A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone. Cones that are homogeneous and self-dual are called symmetric. Conic optimization problems over symmetric cones have been extensively stu…
View article: Bregman Three-Operator Splitting Methods
Bregman Three-Operator Splitting Methods Open
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 steps. The methods extend the primal and dual Condat–Vũ algori…
View article: Linear optimization over homogeneous matrix cones
Linear optimization over homogeneous matrix cones Open
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 cone automorphism that maps one point to the other. Cones that…
View article: Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective
Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective Open
In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization prob…
View article: Bregman three-operator splitting methods
Bregman three-operator splitting methods Open
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 steps. The methods extend the primal and dual Condat-Vu algori…
View article: Bregman primal–dual first-order method and application to sparse semidefinite programming
Bregman primal–dual first-order method and application to sparse semidefinite programming Open
We present a new variant of the Chambolle–Pock primal–dual algorithm with Bregman distances, analyze its convergence, and apply it to the centering problem in sparse semidefinite programming. The novelty in the method is a line search proc…
View article: Regularized Diffusion Adaptation via Conjugate Smoothing
Regularized Diffusion Adaptation via Conjugate Smoothing Open
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 expectation of some loss function with unknown probability di…
View article: Capacities and Optimal Input Distributions for Particle-Intensity Channels
Capacities and Optimal Input Distributions for Particle-Intensity Channels Open
This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the capacity limits as well as properties of the optimal (capacity-achieving) input distributions for such channels.…
View article: Artifact rejection and missing data imputation in cerebral blood flow velocity signals via trace norm minimization
Artifact rejection and missing data imputation in cerebral blood flow velocity signals via trace norm minimization Open
This low-order dynamical approach has ongoing applications in noninvasive intracranial pressure estimation.
View article: Capacities and Optimal Input Distributions for Particle-Intensity\n Channels
Capacities and Optimal Input Distributions for Particle-Intensity\n Channels Open
This work introduces the particle-intensity channel (PIC) as a model for\nmolecular communication systems and characterizes the capacity limits as well\nas properties of the optimal (capacity-achieving) input distributions for such\nchanne…
View article: Semidefinite programming and experiment design
Semidefinite programming and experiment design Open
Semidefinite programming (SDP) has important applications in optimization problems that involve moment cones or, by duality, cones of nonnegative polynomials. Examples can be found in statistics, signal processing, control, and non-convex …
View article: T-optimal design for multivariate polynomial regression using semidefinite programming
T-optimal design for multivariate polynomial regression using semidefinite programming Open
We consider T-optimal experiment design problems for discriminating multivariate polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets. …
View article: T-optimal designs for multi-factor polynomial regression models via a semidefinite relaxation method
T-optimal designs for multi-factor polynomial regression models via a semidefinite relaxation method Open
We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets. …
View article: Douglas-Rachford splitting for a Lipschitz continuous and a strongly monotone operator
Douglas-Rachford splitting for a Lipschitz continuous and a strongly monotone operator Open
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 maximally monotone operators. Recent results concerned with l…
View article: Douglas-Rachford splitting for a Lipschitz continuous and a strongly\n monotone operator
Douglas-Rachford splitting for a Lipschitz continuous and a strongly\n monotone operator Open
The Douglas-Rachford method is a popular splitting technique for finding a\nzero of the sum of two subdifferential operators of proper closed convex\nfunctions; more generally two maximally monotone operators. Recent results\nconcerned wit…
View article: Centralized network utility maximization over aggregate flows
Centralized network utility maximization over aggregate flows Open
We study a network utility maximization (NUM) decomposition in which the set of flow rates is grouped by source-destination pairs. We develop theorems for both single-path and multipath cases, which relate an arbitrary NUM problem involvin…
View article: Semidefinite representations of gauge functions for structured low-rank matrix decomposition
Semidefinite representations of gauge functions for structured low-rank matrix decomposition Open
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless compress…
View article: Diffusion stochastic optimization with non-smooth regularizers
Diffusion stochastic optimization with non-smooth regularizers Open
We develop an effective distributed strategy for seeking the Pareto solution of an aggregate cost consisting of regularized risks. The focus is on stochastic optimization problems where each risk function is expressed as the expectation of…