Related papers: Initial Value Problems for Some Functional Equatio…
Maximization and minimization problems of the principle eigenvalue for divergence form second order elliptic operators with the Dirichlet boundary condition are considered. The principal eigen map of such elliptic operators is introduced…
We consider separable nonconvex optimization problems under affine constraints. For these problems, the Shapley-Folkman theorem provides an upper bound on the duality gap as a function of the nonconvexity of the objective functions, but…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
The existence and multiplicity of solutions for a class of non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise in the solution…
In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
In this paper, we prove functional limit theorems for P\'olya urn processes whose number of draws and initial number of balls tend to infinity together. This is motivated by recent work of Borovkov [5], where they prove a functional limit…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
We consider the rigorous derivation of asymptotic formulas for initial-boundary value problems using the nonlinear steepest descent method. We give detailed derivations of the asymptotics in the similarity and self-similar sectors for the…
It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic implications of this idea for diagrams indexed by a finite…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the…
In the field of reinforcement learning (RL), agents are often tasked with solving a variety of problems differing only in their reward functions. In order to quickly obtain solutions to unseen problems with new reward functions, a popular…