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Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
In this contribution we study the singular limit problem of a nonlocal conservation law with a discontinuity in space. The specific choice of the nonlocal kernel involving the spatial discontinuity as well enables it to obtain a maximum…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several applications. In our analysis, a nonlocal vector calculus is exploited to define a weak…
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties…
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar and vector spherical harmonics, a property that facilitates…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…
We suggest a new delooping machine, which is based on recognizing an n-fold loop space by a collection of operations acting on it, like the traditional delooping machines of Stasheff, May, Boardman-Vogt, Segal, and Bousfield. Unlike in the…
We study a non local approximation of the Gaussian perimeter, proving the Gamma convergence to the local one. Surprisingly, in contrast with the local setting, the halfspace turns out to be a volume constrained stationary point if and only…
The quadratic system provided by the Time of Arrival technique can be solved analytically or by optimization algorithms. In practice, a combination of both methods is used. An important problem in quadratic optimization is the possible…
Local constraint is closely related to the gauge field, so constrained models are usually effective low energy descriptions and important in condensed matter physics. On the other hand, local restriction hinders the application of numerical…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…