113 citations · 229 across the 15 of their papers we have counts for
12 papers · 1 filter
Nonlinear conjugate gradient methods: worst-case convergence rates via computer-assisted analyses
Shuvomoy Das Gupta, Robert M. Freund, Xu Andy Sun +1
We propose a computer-assisted approach to the analysis of the worst-case convergence of nonlinear conjugate gradient methods (NCGMs). Those methods are known for their generally g…
Analysis of the Frank-Wolfe Method for Convex Composite Optimization involving a Logarithmically-Homogeneous Barrier
Renbo Zhao, Robert M. Freund
We present and analyze a new generalized Frank-Wolfe method for the composite optimization problem , where is a -loga…
An Oblivious Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities
Jourdain Lamperski, Robert M. Freund, Michael J. Todd
The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of linear inequalities in variables when its set of solutio…
Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods
Robert M. Freund, Paul Grigas, Rahul Mazumder
Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimi…
Generalized Stochastic Frank-Wolfe Algorithm with Stochastic "Substitute" Gradient for Structured Convex Optimization
Haihao Lu, Robert M. Freund
The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a…
Accelerating Greedy Coordinate Descent Methods
Haihao Lu, Robert M. Freund, Vahab Mirrokni
We study ways to accelerate greedy coordinate descent in theory and in practice, where "accelerate" refers either to convergence in theory, in practice, or both. We intr…
Relatively-Smooth Convex Optimization by First-Order Methods, and Applications
Haihao Lu, Robert M. Freund, Yurii Nesterov
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some…
An Extended Frank-Wolfe Method with "In-Face" Directions, and its Application to Low-Rank Matrix Completion
Robert M. Freund, Paul Grigas, Rahul Mazumder
Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensio…
New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure
Robert M. Freund, Haihao Lu
Motivated by recent work of Renegar, we present new computational methods and associated computational guarantees for solving convex optimization problems using first-order methods…
Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design
Han Men, Robert M. Freund, Ngoc C. Nguyen +2
It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological li…
New Analysis and Results for the Frank-Wolfe Method
Robert M. Freund, Paul Grigas
We present new results for the Frank-Wolfe method (also known as the conditional gradient method). We derive computational guarantees for arbitrary step-size sequences, which are t…
Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods
Han Men, Ngoc-Cuong Nguyen, Robert M. Freund +2
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization pro…