Related papers: A Primal-dual Forward-backward Splitting Method fo…
We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation…
This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…
In this paper, we present a neural path guiding method to aid with Monte Carlo (MC) integration in rendering. Existing neural methods utilize distribution representations that are either fast or expressive, but not both. We propose a…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
The Potts model has many applications. It is equivalent to some min-cut and max-flow models. Primal-dual algorithms have been used to solve these problems. Due to the special structure of the models, convergence proof is still a difficult…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational…
In this paper we demonstrate that multi-modal Probability Distribution Functions (PDFs) may be efficiently sampled using an algorithm originally developed for numerical integrations by Monte-Carlo methods. This algorithm can be used to…
We propose and analyze a versatile and general algorithm called nonlinear forward-backward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto…
In this paper, we propose a model-based machine-learning approach for dual-polarization systems by parameterizing the split-step Fourier method for the Manakov-PMD equation. The resulting method combines hardware-friendly time-domain…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
We propose a Forward-Backward Truncated-Newton method (FBTN) for minimizing the sum of two convex functions, one of which smooth. Unlike other proximal Newton methods, our approach does not involve the employment of variable metrics, but is…
Large-scale multi-objective optimization poses challenges to existing evolutionary algorithms in maintaining the performances of convergence and diversity because of high dimensional decision variables. Inspired by the motion of particles…
In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical…
We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal…