Related papers: A novel Lagrange Multiplier approach with relaxati…
We study the phase retrieval problem, which solves quadratic system of equations, i.e., recovers a vector $\boldsymbol{x}\in \mathbb{R}^n$ from its magnitude measurements $y_i=|\langle \boldsymbol{a}_i, \boldsymbol{x}\rangle|, i=1,..., m$.…
We propose in this paper a new minimization algorithm based on a slightly modified version of the scalar auxiliary variable (SAV) approach coupled with a relaxation step and an adaptive strategy. It enjoys several distinct advantages over…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
The gradient flow is a valuable tool for the lattice community, with applications from scale-setting to implementing chiral fermions. Here I focus on the gradient flow as a means to suppress power-divergent mixing. Power-divergent mixing…
In this paper, we propose a novel family of high-order numerical schemes for the gradient flow models based on the scalar auxiliary variable (SAV) approach, which is named the high-order scalar auxiliary variable (HSAV) method. The newly…
This work focuses on the numerical computation of defocusing action ground states for rotating nonlinear Schr\"odinger equations (RNLS) using a direct gradient flow (DGF) method. We address theoretical gaps in the existing literature…
This paper continues to study linear and unconditionally modified-energy stable (abbreviated as SAV-GL) schemes for the gradient flows. The schemes are built on the SAV technique and the general linear time discretizations (GLTD) as well as…
The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline SAV method can keep a modified energy dissipation law but…
We establish a general framework for developing, efficient energy stable numerical schemes for gradient flows and develop three classes of generalized scalar auxiliary variable approaches (G-SAV). Numerical schemes based on the G-SAV…
The scalar auxiliary variable (SAV) approach is a highly efficient method widely used for solving gradient flow systems. This approach offers several advantages, including linearity, unconditional energy stability, and ease of…
In this paper, we consider numerical approximations for the optimal partition problem using Lagrange multipliers. By rewriting it into constrained gradient flows, three and four steps numerical schemes based on the Lagrange multiplier…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
In a previous paper, we have achieved the performance analysis of staggered Lagrange-remap schemes, a class of solvers widely used for Hydrodynamics applications. This paper is devoted to the rethinking and redesign of the Lagrange-remap…
In this paper, we propose novel algorithms integrated projection-free techniques with accelerated gradient flows to minimize bending energies for nonlinear plates with non-convex metric constraints. We discuss the stability and constraint…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…
The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained…
This paper presents a new algorithm, termed \emph{truncated amplitude flow} (TAF), to recover an unknown vector $\bm{x}$ from a system of quadratic equations of the form $y_i=|\langle\bm{a}_i,\bm{x}\rangle|^2$, where $\bm{a}_i$'s are given…
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…