Complexity of normalized stochastic first-order methods with momentum under heavy-tailed noise
In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically updated algorithmic parameters and do not require explicit knowledge of problem-dependent quantities such as the Lipschitz constant or noise bound. We establish first-order oracle complexity results for finding … Read more
First-order methods for stochastic and finite-sum convex optimization with deterministic constraints
In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an \(\epsilon\)-expectedly feasible stochastic optimal solution, in which the expected constraint violation and expected optimality gap are both within a prescribed tolerance ϵ. However, in many practical applications, constraints must be nearly … Read more
Best-Response Dynamics for Large-Scale Integer Programming Games with Applications to Aquatic Invasive Species Prevention
This paper presents a scalable algorithm for computing the best pure Nash equilibrium (PNE) in large-scale integer programming games (IPGs). While recent advances in IPG algorithms are extensive, existing methods are limited to a small number of players, typically 𝑛 = 2, 3. Motivated by a county-level aquatic invasive species (AIS) prevention problem involving 84 … Read more
A Variational Analysis Approach for Bilevel Hyperparameter Optimization with Sparse Regularization
We study a bilevel optimization framework for hyperparameter learning in variational models, with a focus on sparse regression and classification tasks. In particular, we consider a weighted elastic-net regularizer, where feature-wise regularization parameters are learned through a bilevel formulation. A key novelty of our approach is the use of a Forward-Backward (FB) reformulation of the … Read more
Lipschitz Stability for a Class of Parametric Optimization Problems with Polyhedral Feasible Set Mapping
This paper is devoted to the Lipschitz analysis of the solution sets and optimal values for a class of parametric optimization problems involving a polyhedral feasible set mapping and a quadratic objective function with arametric linear part. Recall that a multifunction is said to be polyhedral if its graph is the union of finitely many polyhedral … Read more
Novel closed-loop controllers for fractional linear quadratic tracking systems
A new method for finding closed-loop optimal controllers of fractional tracking quadratic optimal control problems is introduced. The optimality conditions for the fractional optimal control problem are obtained. Illustrative examples are presented to show the applicability and capabilities of the method. ArticleDownload View PDF
Identifying Regions Vulnerable to Obstetric Unit Closures using Facility Location Modeling with Patient Behavior
Limited geographic access to obstetric care prevents some pregnant people from receiving timely and risk-appropriate services. This challenge is especially acute in rural areas, where rural residents often travel far distances to obstetric care. Furthermore, obstetric access is worsening due to the growing number of closures of rural hospitals’ obstetric units, often due to financial … Read more
Efficient QUIC-Based Damped Inexact Iterative Reweighting for Sparse Inverse Covariance Estimation with Nonconvex Partly Smooth Regularization
In this paper, we study sparse inverse covariance matrix estimation incorporating partly smooth nonconvex regularizers. To solve the resulting regularized log-determinant problem, we develop DIIR-QUIC—a novel Damped Inexact Iteratively Reweighted algorithm based on QUadratic approximate Inverse Covariance (QUIC) method. Our approach generalizes the classic iteratively reweighted \(\ell_1\) scheme through damped fixed-point updates. A key novelty … Read more
A Dynamic Strategic Plan for Transition to Campus-Scale Clean Electricity Using Multi-Stage Stochastic Programming
The decarbonization of energy systems at energy-intensive sites is an essential component of global climate mitigation, yet such transitions involve substantial capital requirements, ongoing technological progress, and the operational complexities of renewable integration. This study presents a dynamic strategic planning framework that applies multi-stage stochastic programming to guide clean electricity transitions at the campus level. … Read more