Related papers: Dynamic Matrix Inverse: Improved Algorithms and Ma…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…

Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However, many DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…

As the pace of AI technology continues to accelerate, more tools have become available to researchers to solve longstanding problems, Hybrid approaches available today continue to push the computational limits of efficiency and precision.…

Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…

Inverse kinematics is a fundamental problem for articulated robots: fast and accurate algorithms are needed for translating task-related workspace constraints and goals into feasible joint configurations. In general, inverse kinematics for…

Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

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, various instances of the problem have been widely studied in…

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…

Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…

We revisit the online dynamic acknowledgment problem. In the problem, a sequence of requests arrive over time to be acknowledged, and all outstanding requests can be satisfied simultaneously by one acknowledgement. The goal of the problem…

The idealization of a static machine-learned model, trained once and deployed forever, is not practical. As input distributions change over time, the model will not only lose accuracy, any constraints to reduce bias against a protected…

Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to…