885 citations · 3.5k across the 45 of their papers we have counts for
17 papers · 1 filter
Dimension-Free Descriptions of Convex Sets
Eitan Levin, Venkat Chandrasekaran
Convex sets arising in a variety of applications are well-defined for every relevant dimension. Examples include the simplex and the spectraplex that correspond to probability dist…
Optimal Regularization for a Data Source
Oscar Leong, Eliza O'Reilly, Yong Sheng Soh +1
In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment criteria that enforce data fidelity with a regularizer that promotes des…
Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP
Mareike Dressler, André Uschmajew, Venkat Chandrasekaran
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The appr…
Spectrahedral Regression
Eliza O'Reilly, Venkat Chandrasekaran
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regress…
Terracini Convexity
James Saunderson, Venkat Chandrasekaran
We present a generalization of the notion of neighborliness to non-polyhedral convex cones. Although a definition of neighborliness is available in the non-polyhedral case in the l…
A Note on Convex Relaxations for the Inverse Eigenvalue Problem
Utkan Candogan, Yong Sheng Soh, Venkat Chandrasekaran
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications,…
Signomial and Polynomial Optimization via Relative Entropy and Partial Dualization
Riley Murray, Venkat Chandrasekaran, Adam Wierman
We describe a generalization of the Sums-of-AM/GM Exponential (SAGE) relaxation methodology for obtaining bounds on constrained signomial and polynomial optimization problems. Our…
Newton Polytopes and Relative Entropy Optimization
Riley Murray, Venkat Chandrasekaran, Adam Wierman
Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications in optimization. We study the question of certifying no…
Learning Semidefinite Regularizers
Yong Sheng Soh, Venkat Chandrasekaran
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are b…
Finding Planted Subgraphs with Few Eigenvalues using the Schur-Horn Relaxation
Utkan Onur Candogan, Venkat Chandrasekaran
Extracting structured subgraphs inside large graphs - often known as the planted subgraph problem - is a fundamental question that arises in a range of application domains. This pr…
Relative Entropy Relaxations for Signomial Optimization
Venkat Chandrasekaran, Parikshit Shah
Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable…
Regularization for Design
Nikolai Matni, Venkat Chandrasekaran
When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between the…
Conic Geometric Programming
Venkat Chandrasekaran, Parikshit Shah
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefin…
Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting
James Saunderson, Venkat Chandrasekaran, Pablo A. Parrilo +1
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in a…
Convex Graph Invariants
Venkat Chandrasekaran, Pablo A. Parrilo, Alan S. Willsky
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper w…
The Convex Geometry of Linear Inverse Problems
Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo +1
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smal…
Rank-Sparsity Incoherence for Matrix Decomposition
Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Parrilo +1
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-ran…