We establish rigorously convergence of a semi-discrete upwind scheme for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0 with u|t=0 = u0 and ut|t=0 = v0. Introducing Riemann invariants R = ut + cux and S = ut − cux, the variational wave equation is equivalent to Rt − cRx = c̃(R2 − S2) and St + cSx = −c̃(R2 − S2) with c̃ = c′/(4c). An upwind scheme is defined for this system. We ass...

In this paper we present a primal interior-point hybrid proximal extragradient (HPE) method for solving a monotone variational inequality over a closed convex set endowed with a selfconcordant barrier and whose underlying map has Lipschitz continuous derivative. In contrast to the method of [7] in which each iteration required an approximate solution of a linearized variational inequality over ...

For optimal control problems with set-valued control constraints and pure state constraints we propose new second-order necessary optimality conditions. In addition to the usual second-order derivative of the Hamiltonian, these conditions contain extra terms involving secondorder tangents to the set of feasible trajectory-control pairs at the extremal process under consideration. The second-ord...

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so–called conserved Noether currents. It turns out that along any section of the relevant gauge–natural bundle this density is the divergence of a skew–symmetric (ten-sor) density, which is called a superpotential for the conserved currents. We describe ...

A uni® ed review of various Kohn variational methods for scattering calculations is presented using appropriate Bloch operators. Previous expressions are generalized slightly to use either an in® nite range or a ® nite range of the scattering coordinate, or to use a basis set with non-® xed log derivative boundary conditions. A non-variationalmethod (method of moments) is used in the derivation...

We present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a class of damped vibration problems on time scale , uΔ 2 t w t uΔ σ t ∇F σ t , u σ t , Δ-a.e. t ∈ 0, T κ , u 0 − u T 0, uΔ 0 − uΔ T 0, where uΔ t denotes the delta or Hilger derivative of u at t, uΔ 2 t uΔ Δ t , σ is the forward jump operator, T is a positive constant, w ∈ R ...

We present two new methods for inference in Gaussian process (GP) models with general nonlinear likelihoods. Inference is based on a variational framework where a Gaussian posterior is assumed and the likelihood is linearized about the variational posterior mean using either a Taylor series expansion or statistical linearization. We show that the parameter updates obtained by these algorithms a...

The variation procedure on a teleparallel manifold is studied. The main problem is the non-commutativity of the variation with the Hodge dual map. We establish certain useful formulas for variations and restate the master formula due to Hehl and his collaborates. Our approach is different and sometimes easier for applications. By introducing the technique of the variational matrix we find neces...

Image fusion and denoising are significant in image processing because of the availability of multi-sensor and the presence of the noise. The first-order and second-order gradient information have been effectively applied to deal with fusing the noiseless source images. In this paper, due to the advantage of the fraction-order derivative, we first integrate the fractionalorder gradients of nois...

A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead, it is solely based on calculus, variational calculus, and linear algebra. Densities are constructed as linear combinations of scaling homogeneous terms with...