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We present a scalability study of Golub-Kahan bidiagonalization for the parallel iterative solution of symmetric indefinite linear systems with a 2x2 block structure. The algorithms have been implemented within the parallel numerical…

Numerical Analysis · Mathematics 2020-01-29 Carola Kruse , Masha Sosonkina , Mario Arioli , Nicolas Tardieu , Ulrich Ruede

This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…

Optimization and Control · Mathematics 2026-05-14 Moisés R. C. do Monte , Rodrigo B. Moreira , Valeriano A. de Oliveira

Current state of the art preconditioners for the reduced Hessian and the Karush-Kuhn-Tucker (KKT) operator for large scale inverse problems are typically based on approximating the reduced Hessian with the regularization operator. However,…

Numerical Analysis · Mathematics 2017-08-03 Nick Alger , Umberto Villa , Tan Bui-Thanh , Omar Ghattas

This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…

Optimization and Control · Mathematics 2026-01-08 Roland Schwan , Daniel Kuhn , Colin N. Jones

This paper presents efforts to improve the hierarchical parallelism of a two scale simulation code. Two methods to improve the GPU parallel performance were developed and compared. The first used the NVIDIA Multi-Process Service and the…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-15 Jacob Merson , Mark S. Shephard

We develop a novel switching dynamics that converges to the Karush-Kuhn-Tucker (KKT) point of a nonlinear optimisation problem. This new approach is particularly notable for its lower dimensionality compared to conventional primal-dual…

Optimization and Control · Mathematics 2026-02-03 Joel Ferguson , Saeed Ahmed , Juan E. Machado , Michele Cucuzzella , Jacquelien M. A. Scherpen

We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers to efficiently address complex combinatorial optimization problems. Traditional Quantum Local Search…

Quantum Physics · Physics 2024-06-11 Chen-Yu Liu , Kuan-Cheng Chen

This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…

Optimization and Control · Mathematics 2025-12-12 Jianting Pan , Ming Yan

Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…

Numerical Analysis · Mathematics 2025-12-10 Teoman Toprak , Florian Kummer

We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…

Optimization and Control · Mathematics 2024-08-06 João Sousa-Pinto , Dominique Orban

In this paper, we propose a parallel shooting algorithm for solving nonlinear model predictive control problems using sequential quadratic programming. This algorithm is built on a two-phase approach where we first test and assess…

Systems and Control · Electrical Eng. & Systems 2023-07-21 P. C. N. Verheijen , M. Haghi , M. Lazar , D. Goswami

In the recent paper of Giorgi, Jim\'enez and Novo (J Optim Theory Appl 171:70--89, 2016), the authors introduced the so-called approximate Karush-Kuhn-Tucker (AKKT) condition for smooth multiobjective optimization problems and obtained some…

Optimization and Control · Mathematics 2018-04-16 Nguyen Van Tuyen , Jen-Chih Yao , Ching-Feng Wen

In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…

Optimization and Control · Mathematics 2024-10-07 Songqiang Qiu , Vyacheslav Kungurtsev

In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible…

Optimization and Control · Mathematics 2024-05-28 Kangyu Lin , Toshiyuki Ohtsuka

We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…

Optimization and Control · Mathematics 2025-05-28 Lauren Conger , Franca Hoffmann , Ricardo Baptista , Eric Mazumdar

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

Mathematical Software · Computer Science 2008-06-12 Alfredo Buttari , Julien Langou , Jakub Kurzak , Jack Dongarra

In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is…

Numerical Analysis · Mathematics 2016-01-12 Alejandra Gaitán Montejo , Octavio A. Michel-Manzo , César A. Terrero-Escalante

Leveraging Trace Theory, we investigate the efficient parallelization of direct solvers for large linear equation systems. Our focus lies on a multi-frontal algorithm, and we present a methodology for achieving near-optimal scheduling on…

Numerical Analysis · Mathematics 2023-06-16 Jan Trynda , Maciej Woźniak , Sergio Rojas

Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial…

Optimization and Control · Mathematics 2026-03-20 Julian Martinez , Kooktae Lee

We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…

Symbolic Computation · Computer Science 2019-06-04 Mohammadali Asadi , Alexander Brandt , Robert H. C. Moir , Marc Moreno Maza , Yuzhen Xie