Stochastic programming

Kall, Peter

doi:10.1016/0377-2217(82)90152-7

Cited by 124 publications

(82 citation statements)

References 21 publications

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“…Several introductory texts cover the topic, including Birge andLouveaux (1997), Infanger (1994), and Kall and Wallace (1994). These texts are focused on general methods for certain classes of stochastic programs.…”

Section: Robert W Brennan Department Of Mechanical and Manufacturingmentioning

confidence: 99%

Book Reviews

Xue

2003

Interfaces

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The range of books reviewed is wide, covering theory and applications in operations research, statistics, management science, econometrics, mathematics, computers, and information systems (no software is reviewed). In addition, we include books in other fields that emphasize technical applications. Publishers who wish to have their books reviewed should send them to Professor Benjamin Lev. We list the books received; not all books received can be reviewed because space is limited. Those who would like to review books are urged to send me their names, addresses, and specific areas of expertise. We commission all reviews and do not accept unsolicited book reviews. Readers are encouraged to suggest books that might be reviewed or to ask publishers to send me copies of such books. The authors or editors of the books reviewed in this issue are Jacek Blazewicz, Klaus H. Ecker, Erwin Pesch, Guenter Schmidt, Jan Weglarz, Eric V. Denardo, Zbigniew Michalewicz, David B. Fogel, Tan Miller, Christoph Schneeweiss, Dileep R. Sule, Stanislav Uryasev, and Panos M. Pardalos.

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Section: Robert W Brennan Department Of Mechanical and Manufacturingmentioning

confidence: 99%

Book Reviews

Xue

2003

Interfaces

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“…There are reasons to believe that the value T does not matter for determining the robust plan X, provided T is large enough, and that the solution to (25){ (27) To avoid some terminal e ects associated with the fact that the vehicles that start late cannot make it to the destination anyway, and therefore choose short arcs, we may augment (25){(27) with terminal conditions: Zì j (t) = Xì j ; t = T ; T + 1; : : :; T 1; T; (i; j) 2 A; (28) where is some constant (for example, the maximum travel time on the arcs). In fact, by choosing T (or ) one may change the allowed length of the transient period, before the ow settles on the new steady-state solution.…”

Section: Stochastic Models In Gamsmentioning

confidence: 99%

“…Problem (29){(31) is similar to two-stage stochastic programming problems (see 25,35,43]). Much is known about these problems, and e cient solution techniques exist that exploit the structure of the model in question (see 26,43] and the references therein).…”

Section: Stochastic Models In Gamsmentioning

confidence: 99%

Traffic Modeling and Variational Inequalities Using GAMS

Dirkse

Ferris

1998

Operations Research and Decision Aid Methodologies in Traffic and Transportation Management

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We describe how several tra c assignment and design problems can be formulated within the GAMS modeling language using newly developed modeling and interface tools. The fundamental problem is user equilibrium, where multiple drivers compete noncooperatively for the resources of the tra c network. A description of how these models can be written as complementarity problems, variational inequalities, mathematical programs with equilibrium constraints, or stochastic linear programs is given. At least one general purpose solution technique for each model format is brie y outlined. Some observations relating to particular model solutions are drawn.

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“…SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLPs) [7,8,9,17,20]. Alternatively, SSDPs may be viewed as an extension of (deterministic) semidefinite programs (SDPs) [1,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

Ariyawansa

Zhu

2010

Math. Comp.

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Abstract. Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDPs). SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLPs). Zhao has derived a decomposition algorithm for SLPs based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Ozevin have extended the work of Zhao to the case of SSDPs to derive a polynomial logarithmic barrier decomposition algorithm for SSDPs. An alternative to the logarithmic barrier is the volumetric barrier of Vaidya. There is no work based on the volumetric barrier analogous to that of Zhao for SLPs or to the work of Mehrotra andÖzevin for SSDPs. The purpose of this paper is to derive a class of volumetric barrier decomposition algorithms for SSDPs, and to prove polynomial complexity of certain members of the class.

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Stochastic programming

Cited by 124 publications

References 21 publications

Book Reviews

Book Reviews

Traffic Modeling and Variational Inequalities Using GAMS

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

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