Related papers: The simultaneous asymmetric perturbation method fo…
In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…
We examine Serrin's classical overdetermined problem under a perturbation of the Neumann boundary condition. The solution of the problem for a constant Neumann boundary condition exists provided that the underlying domain is a ball. The…
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provides a systematic error analysis for IBIMs on uniform…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
In this article we continue our investigation of the thin obstacle problem with variable coefficients which was initiated in \cite{KRS14}, \cite{KRSI}. Using a partial Hodograph-Legendre transform and the implicit function theorem, we prove…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
We propose a novel penalty method framework for the non-self-adjoint topology optimization problems, taking compliant mechanism problems as an example, by incorporating a convex nonlocal perimeter approximation scheme. We rigorously analyze…
In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation is a nonlinear singular ordinary differential equation (ODE)…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
This paper deals with the representation and solution of asymmetric Bayesian decision problems. We present a formal framework, termed asymmetric influence diagrams, that is based on the influence diagram and allows an efficient…