We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on variable sample average approximations (VSAA). The control problem aims to minimize the expected computational cost to obtain a...

Krylov subspace methods have proven to be powerful methods for solving sparse linear systems arising in several engineering problems. More recently, these methods have been successfully applied in computational economics, for instance in the solution of forward-looking macroeconometric models...

This paper investigates computational and implementation issues for the valuation of options on three underlying assets, focusing on the use of the finite difference methods. We demonstrate that implicit methods, which have good convergence and stability prooperties, can now be implemented...

The generalized Stokes problem is solved for non-standard boundary conditions. This problem arises after time semi-discretization by ALE method of the Navier–Stokes system, which describes the flow of two immiscible fluids with similar densities but different viscosities in a horizontal pipe,...

In this paper, we propose interior-point algorithms for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$P_* (\kappa )$$</EquationSource> </InlineEquation>-linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functions. We show that if a strictly feasible starting point is available,...</equationsource></inlineequation>

Приводится система уравнений и неравенств, описывающая потокораспределение в трубопроводных системах с автоматическими регуляторами расхода на некоторых...

We present a variant of the Cholesky factorization for block tridiagonal positive definite matrices. We show that a suitable ordering of block pivots makes it possible to parallelize the linear algebra on a multiple instruction multiple data (MIMD) processor achitecture. The technique applies to...

We extend the two similar interior-point approaches to sensitivity analysis originally developed for linear programs to those for convex quadratic programs, where the first approach is the ∊-sensitivity analysis and the other is Yildirim and Todd's. We study the relationship between the bounds...

In this paper, by using a modified smoothing function, we propose a new continuation method for complementarity problems with R0-function and P0-function in the absence of strict complementarity. At each iteration, the continuation method solves one linear system of equations and performs one...

∊-Sensitivity analysis (∊-SA) is a kind of method to perform sensitivity analysis for linear programming. Its main advantage is that it can be directly applied for interior-point methods with a little computation. In this paper, we discuss the property of ∊-SA analysis and its relationship...