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Polynomial Cutting Plane Algorithms for Two-Stage Stochastic Linear Programs Based

Summary: Polynomial Cutting Plane Algorithms for
Two-Stage Stochastic Linear Programs Based
on Ellipsoids, Volumetric Centers and
Analytic Centers
K. A. Ariyawansa a,,1
aDepartment of Mathematics, Washington State University, Pullman, WA
99164-3113, USA.
P. L. Jiang b,2
bProfessional Services, Delta Dental Plan of Minnesotta, 3560 Delta Dental Drive,
eagan, MN 55122-3166, USA.
Traditional simplex-based algorithms for two-stage stochastic linear programs can
be broadly divided into two groups: (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
group (b) are in general preferred. In 1988, following the work of Karmarkar for
general linear programs, Birge and Qi [11] proposed a specialization of Karmarkar's
algorithm for two-stage stochastic linear programs. The algorithm of Birge and
Qi [11] is the first interior point analog of group (a). Several other authors have


Source: Ariyawansa, Ari - Department of Mathematics, Washington State University


Collections: Mathematics