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There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…

We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…

Efficient nonlinearity compensation in fiber-optic communication systems is considered a key element to go beyond the "capacity crunch''. One guiding principle for previous work on the design of practical nonlinearity compensation schemes…

We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…

A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However,…

Deep neural networks (DNN) have achieved remarkable success in various fields, including computer vision and natural language processing. However, training an effective DNN model still poses challenges. This paper aims to propose a method…

Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…

Deep Neural Networks (DNNs) outshine alternative function approximators in many settings thanks to their modularity in composing any desired differentiable operator. The formed parametrized functional is then tuned to solve a task at hand…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving direct current optimal power flow (DC-OPF) problems. DeepOPF is inspired by the observation that solving DC-OPF for a given power network is equivalent to characterizing…

This paper presents a new convergent Plug-and-Play (PnP) algorithm. PnP methods are efficient iterative algorithms for solving image inverse problems formulated as the minimization of the sum of a data-fidelity term and a regularization…

The densest k-subgraph (DkS) problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant gap between known upper and lower bounds for DkS: the…

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of…

Iterative differential approximation methods that rely upon backpropagation have enabled the optimization of neural networks; however, at present, they remain computationally expensive, especially when training models at scale. In this…

We study the classical Node-Disjoint Paths (NDP) problem: given an $n$-vertex graph $G$ and a collection $M=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of vertices of $G$ called demand pairs, find a maximum-cardinality set of node-disjoint…

We study the design of polylogarithmic depth algorithms for approximately solving packing and covering semidefinite programs (or positive SDPs for short). This is a natural SDP generalization of the well-studied positive LP problem.…

Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so…

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving security-constrained direct current optimal power flow (SC-DCOPF) problems, which are critical for reliable and cost-effective power system operation.DeepOPF is inspired…