相关论文: Efficient solvers for Armijo's backtracking proble…

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…

Many popular first order algorithms for convex optimization, such as forward-backward splitting, Douglas-Rachford splitting, and the alternating direction method of multipliers (ADMM), can be formulated as averaged iteration of a…

The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The…

A new recalibration post-processing method is presented to improve the quality of the posterior approximation when using Approximate Bayesian Computation (ABC) algorithms. Recalibration may be used in conjunction with existing…

Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive…

Deep learning models in large-scale machine learning systems are often continuously trained with enormous data from production environments. The sheer volume of streaming training data poses a significant challenge to real-time training…

The classical convergence analysis of quasi-Newton methods assumes that the function and gradients employed at each iteration are exact. In this paper, we consider the case when there are (bounded) errors in both computations and establish…

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…

This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that…

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

Backpropagation is the default algorithm for training deep neural networks due to its simplicity, efficiency and high convergence rate. However, its requirements make it impossible to be implemented in a human brain. In recent years, more…

Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling…

First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…

The accuracy of information transmission while solving domain decomposed problems is crucial to smooth transition of a solution around the interface/overlapping region. This paper describes a systematical study on an accuracy enhancing…