Related papers: Level Set Jet Schemes for Stiff Advection Equation…
In this paper, a methodology for modelling two-phase flows based on a conservative level set method in the framework of finite volume method is presented. The novelty of the interface capturing method used here lies on the advection of…
We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf 104},…
Two methods of level set type are proposed for solving the Cauchy problem for an elliptic equation. Convergence and stability results for both methods are proven, characterizing the iterative methods as regularization methods for this…
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
In this paper, a new re-initialization method for the conservative level-set function is put forward. First, it has been shown that the re-initialization and advection equations of the conservative level-set function are mathematically…
This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
We search saddle points for a large class of convex-concave Lagrangian. A generalized explicit iterative scheme based on Arrow-Hurwicz method converges to a saddle point of the problem. We also propose in this work, a convergent…
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…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose a two-stage multiphase semi-supervised classification method for classifying high-dimensional data and…
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse…