Related papers: Finite reduction and Morse index estimates for mec…
In the paper, we derive a sensitivity result for a nonlinear fractional ordinary elliptic system on a bounded interval with Dirichlet boundary conditions. More precisely, using a global implicit function theorem, we show that, for any…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
The reduced vacuum Hamiltonian equations of conformal geometrodynamics of compact manifolds in extrinsic time are written. This is achieved by generalizing the theorem of implicit function derivative to the functional analysis.
We study the Morse index of minimal surfaces with free boundary in a half-space. We improve previous estimates relating the Neumann index to the Dirichlet index and use this to answer a question of Ambrozio, Buzano, Carlotto, and Sharp…
Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…
On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the…
This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…
We describe high order accurate and stable fully-discrete finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a…
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…