Related papers: Explicit continuation methods with L-BFGS updating…

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

This paper investigates a new class of non-convex optimization, which provides a unified framework for linear precoding in single/multi-user multiple-input multiple-output (MIMO) channels with arbitrary input distributions. The new…

Knowledge Tracing (KT) aims to model student's knowledge state and predict future performance to enable personalized learning in Intelligent Tutoring Systems. However, traditional KT methods face fundamental limitations in explainability,…

Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are…

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,r}…

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their…

In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

An additive Runge-Kutta method is used for the time stepping, which integrates the linear stiff terms by an explicit singly diagonally implicit Runge-Kutta (ESDIRK) method and the nonlinear terms by an explicit Runge-Kutta (ERK) method. In…

In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…

In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…

Continual learning aims to alleviate catastrophic forgetting when handling consecutive tasks under non-stationary distributions. Gradient-based meta-learning algorithms have shown the capability to implicitly solve the transfer-interference…

Large-scale pre-trained models such as CLIP excel in transferability and robust generalization across diverse datasets. However, adapting these models to new datasets or domains is computationally costly, especially in low-resource or…

Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta…

We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an $L^2$ neighborhood of a local solution that satisfies no-gap second-order sufficient…

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…