Related papers: Fej\'er* monotonicity in optimization algorithms
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…
In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $C$. We assume that the set $C$ can be outerly…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…
Machine learning frameworks adopt iterative optimizers to train neural networks. Conventional eager execution separates the updating of trainable parameters from forward and backward computations. However, this approach introduces…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…
We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time…
We propose a variable metric extension of the forward--backward-forward algorithm for finding a zero of the sum of a maximally monotone operator and a Lipschitzian monotone operator in Hilbert spaces. In turn, this framework provides a…
Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…
Analytic continuation aims to reconstruct real-time spectral functions from imaginary-time Green's functions; however, this process is notoriously ill-posed and challenging to solve. We propose a novel neural network architecture, named the…
Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…
This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These…
Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
We give an iteration scheme for finding zeros of maximal monotone operators in Hilbert spaces. We assume that the operator is defined in the whole space. The iterates converge strongly to a solution if there exists any, otherwise they tend…
Firefly algorithms belong to modern meta-heuristic algorithms inspired by nature that can be successfully applied to continuous optimization problems. In this paper, we have been applied the firefly algorithm, hybridized with local search…