Related papers: PDE Acceleration: A convergence rate analysis and …

Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

This study investigates the variational posterior convergence rates of inverse problems for partial differential equations (PDEs) with parameters in Besov spaces $B_{pp}^\alpha$ ($p \geq 1$) which are modeled naturally in a Bayesian manner…

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated…

Decentralized optimization for non-convex problems are now demanding by many emerging applications (e.g., smart grids, smart building, etc.). Though dramatic progress has been achieved in convex problems, the results for non-convex cases,…

In this paper, we present two variants of DCA (Different of Convex functions Algorithm) to solve the constrained sum of differentiable function and composite functions minimization problem, with the aim of increasing the convergence speed…

This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…

This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…

We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main…

We study momentum-based first-order optimization algorithms in which the iterations utilize information from the two previous steps and are subject to an additive white noise. This setup uses noise to account for uncertainty in either…

We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…

The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such…

Based on the method of FGD, we apply the method of adaptive gradient descent which uses different step length at different epoch. Adaptive gradient descent performs much better than FGD in the tests and keeps the guarantee of convergence…

Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…