 
Summary: Polynomial Cutting Plane Algorithms for
Extended LinearQuadratic Problems in
Stochastic Programming based on Ellipsoids,
Volumetric Centers and Analytic Centers 1
K. A. Ariyawansa a,2
and P. L. Jiang b,3
aDepartment of Pure and Applied Mathematics, Washington State University,
Pullman, WA 991643113, U.S.A.
bProfessional Services, Delta Dental Plan of Minnesota, 3560 Delta Dental Drive,
Eagan, MN 551223166, U.S.A
Abstract
In this paper, we consider the extended linearquadratic problems arising in stochas
tic programming. This class of problems is a nonlinear extension of the twostage
stochastic linear programming problem considered in [3]. The work reported in this
paper is an analog of the work in [3] with extensions of the three polynomial cutting
plane algorithms given there to this more general class of problems.
Key words: Stochastic programming, cutting planes, ellipsoid algorithm, analytic center, volumetric
center, structured convex problems, linearquadratic programming.
1 This research was supported in part by NSF Grant CCR9403892.
2 Corresponding author. Email: ari@wsu.edu. URL: http://www.wsu.edu:8080/ari
