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Filtering point targets in highly cluttered and noisy data frames can be very challenging, especially for complex target motions. Fixed motion models can fail to provide accurate predictions, while learning based algorithm can be difficult…

Federated learning (FL) enables distributed model training from local data collected by users. In distributed systems with constrained resources and potentially high dynamics, e.g., mobile edge networks, the efficiency of FL is an important…

In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…

Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and…

This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…

An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Accurate dynamics models are critical for the design of predictive controller for autonomous mobile robots. Physics-based models are often too simple to capture relevant real-world effects, while data-driven models are data-intensive and…

In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…

We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented…

This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

Federated learning (FL) is a promising paradigm to enable collaborative model training with decentralized data. However, the training process of Large Language Models (LLMs) generally incurs the update of significant parameters, which…

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of…

We discuss the distributed matching scheme in accelerators where control of transverse beam phase space, oscillation, and transport is accomplished by flexible distribution of focusing elements beyond dedicated matching sections. Besides…

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…

We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of…

In light of the increased focus on distributed methods, this paper proposes two accelerated subgradient methods and an adaptive penalty parameter scheme to speed-up the convergence of ADMM on the component-based dual decomposition of the…

We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…