Related papers: A Composite Decomposition Method for Large-Scale G…
This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known…
This research paper presents a novel approach to enhance optimization performance through the hybridization of Gaussian Crunching Search (GCS) and Powell's Method for derivative-free optimization. While GCS has shown promise in overcoming…
Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a…
Log-det semidefinite programming (SDP) problems are optimization problems that often arise from Gaussian graphic models. A log-det SDP problem with an l1-norm term has been examined in many methods, and the dual spectral projected gradient…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…
We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Variable aggregation has been largely studied as an important pre-solve algorithm for optimization of linear and mixed-integer programs. Although some nonlinear solvers and algebraic modeling languages implement variable aggregation as a…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
Compressed sensing (CS) is a promising tool for reducing sampling costs. Current deep neural network (NN)-based CS methods face the challenges of collecting labeled measurement-ground truth (GT) data and generalizing to real applications.…
The Security-Constrained Unit Commitment (SCUC) problem presents formidable computational challenges due to its combinatorial complexity, large-scale network dimensions, and numerous security constraints. While conventional temporal…
In the era of big data, optimizing large scale machine learning problems becomes a challenging task and draws significant attention. Asynchronous optimization algorithms come out as a promising solution. Recently, decoupled asynchronous…
We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
Domain generalization (DG) aims to improve the generalizability of computer vision models toward distribution shifts. The mainstream DG methods focus on learning domain invariance, however, such methods overlook the potential inherent in…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Granular ball computing (GBC), as an efficient, robust, and scalable learning method, has become a popular research topic of granular computing. GBC includes two stages: granular ball generation (GBG) and multi-granularity learning based on…