Related papers: Approximating evolution operators of linear delay …

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…

We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…

Evolutionary algorithms have been widely applied for solving dynamic constrained optimization problems (DCOPs) as a common area of research in evolutionary optimization. Current benchmarks proposed for testing these problems in the…

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…

We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…

The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…

Curve evolution is often used to solve computer vision problems. If the curve evolution fails to converge, we would not be able to solve the targeted problem in a lifetime. This paper studies the theoretical aspect of the convergence of a…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

In this paper, we extend a class of globally convergent evolution strategies to handle general constrained optimization problems. The proposed framework handles relaxable constraints using a merit function approach combined with a specific…

We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…

We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…