Related papers: Solving discrete constrained problems on de Rham c…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…
Using properties of harmonic functions in multidimensional space, we transform the Hartree-Fock eigenvalue problem into a more tractable eigenvalue problem in which the Laplacian is eliminated. This new formulation may facilitate the…
We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p. We show that the discrete minimizers in the spaces of piecewise…
The systematic method for the conversion of first class constraints to the equivalent set of Abelian one based on the Dirac equivalence transformation is developed. The representation for the corresponding matrix performing this…
We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its…
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
CSPTRQ is an interesting problem and its has attracted much attention. The CSPTRQ is a variant of the traditional PTRQ. As objects moving in a constrained-space are common, clearly, it can also find many applications. At the first sight,…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
We introduce an iterative scheme for discrete convex minimization problems of $p$-Laplace type such as variational graph $p$-Laplace problems and $\ell^p$ regression. In each iteration, the scheme solves only a weighted least-squares…
In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in $H^1$, $H({\rm curl})$, and…
Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We give a damped proximal augmented Lagrangian method (DPALM) for solving problems with a weakly-convex objective and convex linear/nonlinear constraints. Instead of taking a full stepsize, DPALM adopts a damped dual stepsize to ensure the…
The Dirichlet problem on a bounded planar domain is more readily understood and solved for the Laplace operator than it is for a Schrodinger operator. When the potential function is small, we might hope to approximate the solution to the…
We now set up Constraint Closure in a manner consistent with Temporal and Configurational Relationalism. This requires modifying the Dirac Algorithm - which addresses the Constraint Closure Problem facet of the Problem of Time piecemeal -…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…