Related papers: Optimization-based smoothing algorithm for triangl…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on the centralized Method…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…