Related papers: A short report on preconditioned Anderson accelera…

We address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We…

Preconditioners are generally essential for fast convergence in the iterative solution of linear systems of equations. However, the computation of a good preconditioner can be expensive. So, while solving a sequence of many linear systems,…

The Quantum Approximate Optimization Algorithm (QAOA) exhibits significant potential for tackling combinatorial optimization problems. Despite its promise for near-term quantum devices, a major challenge in applying QAOA lies in the cost of…

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly…

In this paper preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of SR1 and BFGS low-rank…

This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…

The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…

We develop a novel approach for confidently accelerating inference in the large and expensive multilayer Transformers that are now ubiquitous in natural language processing (NLP). Amortized or approximate computational methods increase…

Independent component analysis (ICA) has been used in many applications, including self-interference cancellation for in-band full-duplex wireless systems and anomaly detection in industrial internet of things. This paper presents a…

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

In this paper we study a nonlinear dual space preconditioning approach for the relaxed Proximal Point Algorithm (PPA) with application to monotone and relatively cohypomonotone inclusions, called anisotropic PPA. The algorithm is an…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

We describe how the low-rank structure in an SDP can be exploited to reduce the per-iteration cost of a convex primal-dual interior-point method down to $O(n^{3})$ time and $O(n^{2})$ memory, even at very high accuracies. A traditional…

We provide a rounding error analysis of a mixed-precision preconditioned Jacobi algorithm, which uses low precision to compute the preconditioner, applies it at high precision (amounting to two matrix-matrix multiplications) and solves the…

Photoacoustic imaging (PAI) is a non-invasive imaging modality that detects the ultrasound signal generated from tissue with light excitation. Photoacoustic computed tomography (PACT) uses unfocused large-area light to illuminate the target…

Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution…

We give new convergence results of Anderson acceleration for the composite $\max$ fixed point problem. We prove that Anderson(1) and EDIIS(1) are q-linear convergent with a smaller q-factor than existing q-factors. Moreover, we propose a…

Typical pipelines for model geometry generation in computational biomedicine stem from images, which are usually considered to be at rest, despite the object being in mechanical equilibrium under several forces. We refer to the stress-free…