Traditional simplex-basedalgorithms for two-stage stochastic linear programscan be broadly divided into two classes: (a) those that explicitly exploit the structure of the equivalent large-scale linear program and (b) those based on cutting planes (or equivalently on decomposition) that implicitly exploit that structure. Algorithms of class (b) are in… (More)
Burke, Goldstein, Tseng and Ye (Ref. 1) have presented an interesting interior point algorithm for a class of smooth convex minimax problems. They have also presented a complexity analysis leading to a worst-case bound on the total work necessary to obtain a solution within a prescribed tolerance. In this paper we present reenements to the analysis of Burke… (More)
Recently, Bertsimas and Orlin 1] have given polynomial complexity for several combinatorial optimization subproblems using Vaidya's volumetric center algorithm as a subroutine. These complexity results improve on the previously best known for several problems, including for example computing the Held-Karp lower bound for Traveling Sales-person problem and… (More)
We determine the eigenvalues of a Fredholm integral operator of the second kind. The solution of the eigenvalue problem has applications to nding the distribution function of a stochastic integral. The stochastic integral itself represents the asymptotic form of a statistical test. Also discussed are related results for inference and applications.
Burke, Goldstein, Tseng and Ye 4] have presented an interior point algorithm for the smooth convex minimax problem: minimization of the pointwise maximum of n thrice-diierentiable convex functions of m variables. Their algorithm is based on analytic centers. The novel feature of their algorithm relative to several other algorithms based on analytic centers… (More)
We point out several oversights in statements concerning stochastic programming in a paper of Bertsimas and Orlin (this journal, 1994).
In this paper, we consider the extended linear-quadratic problems arising in stochas-tic programming. This class of problems is a nonlinear extension of the two-stage stochastic linear programming problem considered in . The work reported in this paper is an analog of the work in  with extensions of the three polynomial cutting plane algorithms given… (More)