Related papers: Momentum-based Accelerated Mirror Descent Stochast…
A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…
Remote sensing change detection (RSCD) is vital for identifying land-cover changes, yet existing methods, including state-of-the-art State Space Models (SSMs), often lack explicit mechanisms to handle geometric misalignments and struggle to…
Objective functions in large-scale machine-learning and artificial intelligence applications often live in high dimensions with strong non-convexity and massive local minima. First-order methods, such as the stochastic gradient method and…
We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when…
Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…
The recently proposed Muon optimizer updates weight matrices via orthogonalized momentum and has demonstrated strong empirical success in large language model training. However, it remains unclear how to determine the learning rates for…
In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI)…
Stochastic dual coordinate ascent (SDCA) is an effective technique for solving regularized loss minimization problems in machine learning. This paper considers an extension of SDCA under the mini-batch setting that is often used in…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
In this paper, we propose an efficient frontier detector method based on adaptive Rapidly-exploring Random Tree (RRT) for autonomous robot exploration. Robots can achieve real-time incremental frontier detection when they are exploring…
This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk…
Modular reconfigurable manipulators enable quick adaptation and versatility to address different application environments and tailor to the specific requirements of the tasks. Task performance significantly depends on the manipulator's…
End-to-end autonomous driving frameworks enable seamless integration of perception and planning but often rely on one-shot trajectory prediction, which may lead to unstable control and vulnerability to occlusions in single-frame perception.…
Mobile cyberphysical systems have received considerable attention over the last decade, as communication, computing and control come together on a common platform. Understanding the complex interactions that govern the behavior of large…
In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization. Specifically, we propose a new accelerated zeroth-order momentum (Acc-ZOM) method…
Recent multi-task learning studies suggest that linear scalarization, when using well-chosen fixed task weights, can achieve comparable to or even better performance than complex multi-task optimization (MTO) methods. It remains unclear why…
This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…