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Polynomial Cutting Plane Algorithms for Extended Linear-Quadratic Problems in Stochastic Programming based on Ellipsoids, Volumetric Centers and Analytic Centers 1

In this paper, we consider the extended linear-quadratic problems arising in stochastic programming. This class of problems is a nonlinear extension of the two-stage 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.