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Bilevel hyperparameter optimization has received growing attention thanks to the fast development of machine learning. Due to the tremendous size of data sets, the scale of bilevel hyperparameter optimization problem could be extremely…

Optimization and Control · Mathematics 2025-10-27 Yixin Wang , Qingna Li , Liwei Zhang

Complex-Valued Neural Networks (CVNNs) have significant advantages in handling tasks that involve complex numbers. However, existing CVNNs are unable to quantify predictive uncertainty. We propose, for the first time, dropout-based Bayesian…

Hardware Architecture · Computer Science 2026-04-23 Zehuan Zhang , Mark Chen , He Li , Wayne Luk

We present a new approach to parallelization of the first-order backward difference discretization (BDF1) of the time derivative in partial differential equations, such as the nonlinear heat and viscous Burgers equations. The time…

Numerical Analysis · Mathematics 2024-06-04 Nail K. Yamaleev , Subhash Paudel

Counting lattice points within a rational polytope is a foundational problem with applications across mathematics and computer science. A key approach is Barvinok's algorithm, which decomposes the lattice point generating function of cones…

Combinatorics · Mathematics 2025-06-25 Sihao Tao , Guoce Xin , Zihao Zhang

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…

Optimization and Control · Mathematics 2024-12-20 Veronica Piccialli , Jan Schwiddessen , Antonio M. Sudoso

In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to…

Optimization and Control · Mathematics 2024-12-10 Marcin Anholcer , Janos Fülöp

Data mining algorithms are originally designed by assuming the data is available at one centralized site.These algorithms also assume that the whole data is fit into main memory while running the algorithm. But in today's scenario the data…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-12-03 Aruna Govada , Bhavul Gauri , S. K. Sahay

In this paper, we propose a Two-Step Linear Mixing Model (2LMM) that bridges the gap between model complexity and computational tractability. The model achieves this by introducing two distinct scaling steps: an endmember scaling step…

Image and Video Processing · Electrical Eng. & Systems 2025-12-04 Xander Haijen , Bikram Koirala , Xuanwen Tao , Paul Scheunders

The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit…

We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…

Numerical Analysis · Mathematics 2013-03-25 Mårten Gulliksson , Sverker Edvardsson , Andreas Lind

We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…

Optimization and Control · Mathematics 2025-01-22 Stephen P. Boyd , Tetiana Parshakova , Ernest K. Ryu , Jaewook J. Suh

Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…

Data Analysis, Statistics and Probability · Physics 2024-07-24 Judith F. Stein , Aviad Frydman , Richard Berkovits

The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and…

Numerical Analysis · Mathematics 2024-09-05 Tommaso Bevilacqua , Axel Klawonn , Martin Lanser

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…

Numerical Analysis · Mathematics 2023-06-12 Rachel Minster , Zitong Li , Grey Ballard

Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…

Quantum Physics · Physics 2023-11-23 Carlos Bravo-Prieto , Ryan LaRose , M. Cerezo , Yigit Subasi , Lukasz Cincio , Patrick J. Coles

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An…

Optimization and Control · Mathematics 2016-10-21 Sebastian Banert , Radu Ioan Bot

This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are…

Numerical Analysis · Mathematics 2024-10-22 Neethu Suma Raveendran , Md Abdul Aziz , Muhammad Mohebujjaman

Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and…

Optimization and Control · Mathematics 2020-03-04 Bruce A. Cox

This paper considers convex quadratic programs associated with the training of support vector machines (SVM). Exploiting the special structure of the SVM problem a new type of active set method with long cycles and stable rank-one-updates…

Optimization and Control · Mathematics 2025-04-09 Florian Jarre

Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…

Machine Learning · Statistics 2023-12-22 Daniel J. W. Touw , Patrick J. F. Groenen , Yoshikazu Terada