Scalable Convex Methods for Phase Retrieval

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Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optim ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...

The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity as well as faster convergence speed. Moreover, many of ...

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate ...

The ever-increasing requirements for reliability and quality of supply suggest to enable the self-healing features of modern distribution networks. Within the context of Active Distribution Networks (ADNs), new, fast and efficient restoration strategies ca ...

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust met ...

The desire to operate chemical processes in a safe and economically optimal way has motivated the development of so-called real-time optimization (RTO) methods [1]. For continuous processes, these methods aim to compute safe and optimal steady-state set ...

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computati ...

Curvilinear networks are prevalent in nature and span many different scales, ranging from micron-scale neural structures in the brain to petameter-scale dark-matter arbors binding massive galaxy clusters. Reliably reconstructing them in an automated fashio ...

In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensio ...

The self-concordant-like property of a smooth convex func- tion is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self- concordant-like property, this concept has heretofor ...

Scalable Convex Methods for Phase Retrieval

Chattez avec Graph Search

Scalable constrained optimization

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Stochastic distributed learning with gradient quantization and double-variance reduction

Efficient Meso-Scale Modeling of Alkali-Silica-Reaction Damage in Concrete

A first-order primal-dual method with adaptivity to local smoothness

A Newton Frank-Wolfe method for constrained self-concordant minimization

Large Steps in Inverse Rendering of Geometry

Adaptive Gradient Descent without Descent

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Service Restoration in DG-Integrated Distribution Networks Using an Exact Convex OPF Model

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Distributed Modifier-Adaptation Schemes for the Real-Time Optimization of Interconnected Systems in the Presence of Structural Plant-Model Mismatch

Stochastic Three-Composite Convex Minimization

Automated Reconstruction of Evolving Curvilinear Tree Structures

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

Composite convex minimization involving self-concordant-like cost functions