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Mimetic Relaxation Runge Kutta Methods
Linear hyperbolic partial differential equations (PDEs) are known to conserve energy in the absence of a source term. For example, the solution of...
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T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization
We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs...
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Finding an Approximate Riemann Solver via Relaxation: Concept and Advantages
We first explain the general concept of relaxation models using the **-**n model for scalar conservation laws. Then we consider the Suliciu model...
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Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review
Hyperbolic systems with stiff relaxation constitute a wide class of evolutionary partial differential equations which describe several physical...
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Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
We generalize the idea of relaxation time step** methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by...
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Discrete Adjoint Computations for Relaxation Runge–Kutta Methods
Relaxation Runge–Kutta methods reproduce a fully discrete dissipation (or conservation) of entropy for entropy stable semi-discretizations of...
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Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws
Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes,...
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A Second-order Cone Relaxation-Based Branch-and-Bound Algorithm for Complex Quadratic Programs on Acyclic Graphs
Complex quadratically constrained quadratic programs (QCQPs) with underlying acyclic graph structures have special interests in some important...
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Partial Lasserre relaxation for sparse Max-Cut
A common approach to solve or find bounds of polynomial optimization problems like Max-Cut is to use the first level of the Lasserre hierarchy....
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IPRSOCP: A Primal-Dual Interior-Point Relaxation Algorithm for Second-Order Cone Programming
Inspired by the smoothing barrier augmented Lagrangian function in Liu et al. (Math Methods Oper Res 96(3):351–382, 2022), we propose a primal-dual...
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Subordination and memory dependent kinetics in diffusion and relaxation phenomena
The concept of subordination, originally introduced in the probability and stochastic processes theories, has also appeared in analysis of evolution...
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A Strengthened SDP Relaxation for Quadratic Optimization Over the Stiefel Manifold
We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We...
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Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth
A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided....
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A matrix nonconvex relaxation approach to unconstrained binary polynomial programs
This paper is concerned with a class of unconstrained binary polynomial programs (UBPPs), which covers the classical binary quadratic program and has...
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On convergence of waveform relaxation for nonlinear systems of ordinary differential equations
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic...
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Relaxation of the Volume Charge Created by the Electron Flow in Air
AbstractThe process of the relaxation of the volume electric charge formed by high-energy electrons in air is considered. The charge carriers are...
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A Low Mach Number Two-Speed Relaxation Scheme for Ideal MHD Equations
In this workBirke, Claudius weKlingenberg, Christian apply the two-speed relaxation technique to a relaxation system for the compressible ideal...
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Continuous Exact Relaxation and Alternating Proximal Gradient Algorithm for Partial Sparse and Partial Group Sparse Optimization Problems
In this paper, we consider a partial sparse and partial group sparse optimization problem, where the loss function is a continuously differentiable...
