Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic systems embedded is a challenging task. In this article, for any locally Lipschitz continuous mapping between finitedimensional Euclidean spaces, Nesterov’s lexicographic derivatives are shown to b...

We present some new techniques for solving a family (or a sequence of families) of linear systems in which the coefficient matrices differ only by a scalar multiple of the identity (shifted systems). Our goal is to develop methods for shifted systems which have fewer restrictions usually associated with such methods (e.g., all residuals needing to be collinear). The systems are parameterized by i,

Projection techniques are developed for computing approximate solutions to linear systems of the form Ax n = b n , for a sequence n = 1; 2; :::, e.g., arising from time discretization of a partial diierential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system, resulting in signiicantly reduced computatio...

In this paper, we propose a new method for solving general linear systems with several right-hand sides. This method is based on global least squares method and reduces the original matrix to the lower bidiagonal form. We derive a simple recurrence formula for generating the sequence of approximate solutions {Xk}. Some theoretical properties of the new method are discussed and we also show that...

We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to ...

A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary step is fixing some rows of the inverse matrix of SLAEs. The second step consists in calculating solutions for all right-hand sides. For reducing the communic...

This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random variables. Such problems are of interest since the use of Gaussian estimators of random variables is widespread. We introduce algorithms to nd upper bounds on the optimal value of two-stage and multi-stage stochastic (minimization) programs with Gaussian right...

A class of nonlinear nonstationary systems of Persidskii type is studied. The right-hand sides of the systems are represented in the form of linear combinations of sector nonlinearities with time-varying coefficients. It is assumed that the coefficients possess mean values. By means of the Lyapunov direct method, it is proved that if the investigated systems are essentially nonlinear, i.e. the ...

This paper deals with the average-case-analysis of the number of pivot steps required by the simplex method. It generalizes results of Borgwardt (who worked under the assumpution of the rotation-symmetry-model) for the shadow-vertex-algorithm to so-called cylindric distributions. Simultaneously it allows to analyze an extended dimension-by-dimension-algorithm, which solves linear programing pro...

In this survey we address three of the principal algebraic approaches to integer programming. After introducing lattices and basis reduction, we 0rst survey their use in integer programming, presenting among others Lenstra’s algorithm that is polynomial in 0xed dimension, and the solution of diophanine equations using basis reduction. The second topic concerns augmentation algorithms and test s...