This paper is concerned with the numerical approximation of the expected value IE(g(Xt)), where g is a suitable test function and X is the solution of a stochastic differential equation driven by a Lévy process Y . More precisely we consider an Euler scheme or an “approximate” Euler scheme with stepsize 1/n, giving rise to a simulable variable Xn t , and we study the error δn(g) = IE(g(X n t ))...

We consider the numerical solution of differential-algebraic systems of index one given in Kronecker canonical form. The methods described here are derived from the Rosenbrock approach. Hence, they do not require the solution of nonlinear systems of equations but one evaluation of the Jacobian and one LU decomposition per step. By construction, the s-stage method coincides with a solver for non...

We investigate solving semidefinite programs SDPs with an interior point method called SDPCUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that u...

where | · | denotes the `1 norm, ‖·‖ denotes the `2 norm, A is a matrix, b is a vector, and μ is a scalar parameter. This problem is of the form (1) with g(z) = μ|z|, and f(z) = 12‖z− b‖ . More generally, any problem of the form (1) can be solved by FASTA, provided the user can provide function handles to f, g, A and A . The solver FASTA contains numerous enhancements of FBS to improve converge...

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm is its convergence in the presence of degeneracy (which is important since 'practical" problems tend to be degenerate). In this paper, we give new convergence results for this algorithm that do not...

<p style='text-indent:20px;'>We study the problem of minimizing sum two functions. The first function is average a large number nonconvex component functions and second convex (possibly nonsmooth) that admits simple proximal mapping. With diagonal Barzilai-Borwein stepsize for updating metric, we propose variable metric stochastic variance reduced gradient method in mini-batch setting, na...

In this paper, we present an efficient real-time implementation of a broadband algorithm for blind source separation (BSS) of convolutive mixtures. A recently introduced generic BSS framework based on a matrix formulation allows simultaneous exploitation of nonwhiteness and nonstationarity of the source signals using second-order statistics. We demonstrate here that this general scheme leads to...

Various simulation methods for tempered stable random variates with stability index greater than one are investigated with a view towards practical implementation, in particular cases of very small scale parameter, which correspond to increments of a tempered stable Lévy process with a very short stepsize. Methods under consideration are based on acceptance-rejection sampling, a Gaussian approx...