We propose a modification to the simultaneous perturbation stochastic approximation (SPSA) methods based on the comparisons made between the firstand second-order SPSA (1SPSA and 2SPSA) algorithms from the perspective of loss function Hessian. At finite iterations, the accuracy of the algorithm depends on the matrix conditioning of the loss function Hessian. The error of 2SPSA algorithm for a l...

In this paper, we suggest two ways of calculating interpolation models for unconstrained smooth nonlinear optimization when Hessian-vector products are available. The main idea is to interpolate the objective function using a quadratic on set points around current one and concurrently curvature information from Hessian times appropriate vectors, possibly defined by interpolating points. These e...

For functions defined on integer lattice points, discrete versions of the Hessian matrix have been considered in various contexts. In discrete convex analysis, for example, certain combinatorial properties of the discrete Hessian matrices are known to characterize M-convex and L-convex functions, which can be extended to convex functions in real variables. The relationship between convex extens...

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...

Two approximations of the Hessian matrix as limited-memory operators are built from the limited-memoryBFGS inverse Hessian approximationprovided by the minimization code, in view of the speci cation of the inverse analysis/forecast error covariance matrix in variational data assimilation. Some numerical experiments and theoretical considerations lead to reject the limited-memory DFP Hessian app...

Modified Shepard interpolation based on second order Taylor series expansions has proven to be a flexible tool for constructing potential energy surfaces in a range of situations. Extending this to gas-surface dynamics where surface atoms are allowed to move represents a substantial increase in the dimensionality of the problem, reflected in a dramatic increase in the computational cost of the ...

The focus of the present study was to compare ultrastructure in the midguts of larvae of the Hessian fly, Mayetiola destructor (Say), under different feeding regimens. Larvae were either fed on Hessian fly-resistant or -susceptible wheat, and each group was compared to starved larvae. Within 3h of larval Hessian fly feeding on resistant wheat, midgut microvilli were disrupted, and after 6h, mic...

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobiquartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobiquartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (...

We propose a method for computation of the Hessian of axially symmetric functions on the roto-translation group SE(3). Eigendecomposition of the resulting Hessian is then used for curvature estimation of tubular structures, similar to how the Hessian matrix of 2D or 3D image data can be used for orientation estimation. This paper focuses on a new implementation of a Gaussian regularized Hessian...