Related papers: A Unified Theoretic and Algorithmic Framework for …
We propose a prox-regular-type low-rank constrained nonconvex nonsmooth optimization model for Robust Low-Rank Matrix Recovery (RLRMR), i.e., estimate problem of low-rank matrix from an observed signal corrupted by outliers. For RLRMR, the…
Large Language Models (LLMs) have shown remarkable capabilities in solving various programming tasks, such as code generation. However, their potential for code optimization, particularly in performance enhancement, remains largely…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
The popularity of algorithms based on Extreme Learning Machine (ELM), which can be used to train Single Layer Feedforward Neural Networks (SLFN), has increased in the past years. They have been successfully applied to a wide range of…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
Future wireless networks are expected to incorporate diverse services that often lack general mathematical models. To address such black-box network management tasks, the large language model (LLM) optimizer framework, which leverages…
The recent work `A unified Bayesian inference framework for generalized linear models' \cite{meng1} shows that the GLM can be solved via iterating between the standard linear module (SLM) (running with standard Bayesian algorithm) and the…
Reweighted l1-algorithms have attracted a lot of attention in the field of applied mathematics. A unified framework of such algorithms has been recently proposed by Zhao and Li. In this paper we construct a few new examples of reweighted…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
Recently, advanced large language models (LLMs) have emerged at an increasingly rapid pace. However, when faced with complex problems, most users are often unable to provide accurate and effective prompts to interact with LLMs, thus…
This paper investigates two inexact Levenberg-Marquardt (LM) methods for solving systems of nonlinear equations. Both approaches compute approximate search directions by solving the LM linear system inexactly, subject to specific…
Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Mathematical optimization is a powerful tool for structured decision-making across domains such as resource allocation and planning. Formulating optimization models faithful to reality, though, remains a significant bottleneck as it…
This paper develops a generalization of the line-search sequential quadratic programming (SQP) algorithm with $\ell_1$-merit function that uses objective and constraint function approximations with tunable accuracy to solve smooth…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier…