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Stochastic Integer Programming
[chapter]

1992
*
Operations Research Proceedings 1991
*

Polynomial time approximation algorithms and their performance guarantees for

doi:10.1007/978-3-642-46773-8_100
fatcat:nu2euvyzfre6tfvqt2dkxk2xy4
*stochastic*linear and*integer**programming*problems have seen increasing research attention only very recently. ... The reader interested in this issue is referred to surveys on*stochastic**programming*, like the Handbook on*Stochastic**Programming*[38] or the text books [3, 21, 35] . ... Thus, two-stage*stochastic**integer**programming*is in the class N P ♯P . ...##
###
Stochastic Integer Programming
[chapter]

1988
*
Springer Series in Computational Mathematics
*

Polynomial time approximation algorithms and their performance guarantees for

doi:10.1007/978-3-642-61370-8_8
fatcat:k46jjqnrbzdp5iua7s4dgfdkse
*stochastic*linear and*integer**programming*problems have seen increasing research attention only very recently. ... The reader interested in this issue is referred to surveys on*stochastic**programming*, like the Handbook on*Stochastic**Programming*[38] or the text books [3, 21, 35] . ... Thus, two-stage*stochastic**integer**programming*is in the class N P ♯P . ...##
###
Stochastic Integer Programming
[chapter]

2003
*
Handbooks in Operations Research and Management Science
*

##
###
Stochastic Integer Programming by Dynamic Programming
[chapter]

1988
*
Springer Series in Computational Mathematics
*

*Stochastic*

*integer*

*programming*is a suitable tool for modeling hierarchical decision situations with combinatorial features. ... Dynamic

*programming*techniques can be used to exploit the structure of two-stage scheduling, bin packing and multi.knapsack problems. ... By imposing integrality constraints on some of the decision variables we enter the area of

*stochastic*

*integer*

*programming*. ...

##
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Stochastic Dual Dynamic Programming for Multistage Stochastic Mixed-Integer Nonlinear Optimization
[article]

2022
*
arXiv
*
pre-print

In this paper, we study multistage

arXiv:1912.13278v5
fatcat:ylpflyescbbx7dmavgedppdk3e
*stochastic*mixed-*integer*nonlinear*programs*(MS-MINLP). ... We develop*stochastic*dual dynamic*programming*(SDDP) type algorithms with nested decomposition, deterministic sampling, and*stochastic*sampling. ... A multistage*stochastic*mixed-*integer*nonlinear*program*(MS-MINLP) is a sequential decision making problem under uncertainty with both continuous and*integer*decisions and nonconvex nonlinear objective ...##
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Stochastic Packing Integer Programs with Few Queries
[article]

2019
*
arXiv
*
pre-print

We consider a

arXiv:1707.04020v3
fatcat:myc72wakm5cnxovi35pp7ajoru
*stochastic*variant of the packing-type*integer*linear*programming*problem, which contains random variables in the objective vector. ... We also demonstrate our framework by applying it to a variety of*stochastic*combinatorial optimization problems such as matching, matroid, and stable set problems. ... Other variants of the*stochastic*packing*integer**programming*problem with queries have been studied. ...##
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Integer Set Reduction for Stochastic Mixed-Integer Programming
[article]

2016
*
arXiv
*
pre-print

Two-stage

arXiv:1605.05194v1
fatcat:nfwy2ccip5aszmqaclvopmww2e
*stochastic*mixed-*integer**programming*(SMIP) problems with general*integer*variables in the second-stage are generally difficult to solve. ... The basic idea is to consider a small enough subset of feasible*integer*points that is necessary for generating a valid inequality for the*integer*subproblem. ... Introduction A two-stage*stochastic*mixed-*integer**programming*(SMIP) problem involves optimizing the here-and-now (first-stage) costs plus expected future (second-stage) costs. ...##
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Integer programming for weakly coupled stochastic dynamic programs with partial information
[article]

2020
*
arXiv
*
pre-print

Partially observable Markov decision processes (POMDPs) have been introduced to deal with the first challenge, while weakly coupled

arXiv:2012.00645v4
fatcat:btskg7jdt5gipl32t26ct4kes4
*stochastic*dynamic*programs*address the second. ... The first, which can be used independently, is a mixed*integer*linear formulation for generic POMDPs that computes an optimal memoryless policy. ...*Integer**programming*for POMDPs In this section, we provide an*integer*formulation that gives an optimal memoryless policy for P ml as well as valid inequalities. ...##
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Stochastic programming with simple integer recourse

1993
*
Mathematical programming
*

In this paper, we introduce the class of

doi:10.1007/bf01582153
fatcat:2rhuhi5skrgythfd7vrmno2w3u
*stochastic**programs*with simple*integer*recourse, a natural extension of the simple recourse case extensively studied in*stochastic*continuous*programs*. ...*Stochastic**integer**programs*are notoriously difficult. Very few properties are known and solution algorithms are very scarce. ... We call this mathematical*program*a*stochastic*linear*program*with simple*integer*recourse. Sometimes also x is*integer*. In that case, x ∈ IR n 1 + is replaced by x ∈ Z Z n 1 + . ...##
###
Finiteness theorems in stochastic integer programming
[article]

2005
*
arXiv
*
pre-print

We study Graver test sets for families of linear multi-stage

arXiv:math/0502078v1
fatcat:ff4vawhxobd7lbn3wlu2ooy4vq
*stochastic**integer**programs*with varying number of scenarios. ...*integer**program*. ... We also show how to compute H k,∞ (even if only theoretically), and how it can be employed to solve any given particular instance of the given family of (k + 1)-stage*stochastic**integer**programs*. ...##
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Finiteness Theorems in Stochastic Integer Programming

2006
*
Foundations of Computational Mathematics
*

We study Graver test sets for families of linear multi-stage

doi:10.1007/s10208-005-0174-1
fatcat:r7hbpf32z5h5zkzaa6oc4b6sqy
*stochastic**integer**programs*with varying number of scenarios. ... Building Blocks In this section we study multistage*stochastic**integer**programs*. ...*integer**program*. ...##
###
On Generating Lagrangian Cuts for Two-Stage Stochastic Integer Programs
[article]

2022
*
arXiv
*
pre-print

*stochastic*

*integer*

*program*. ... We investigate new methods for generating Lagrangian cuts to solve two-stage

*stochastic*

*integer*

*programs*. ... Introduction We study methods for solving two-stage

*stochastic*

*integer*

*programs*(SIPs) with general mixed-

*integer*first-stage and second-stage variables. ...

##
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Stochastic Packing Integer Programs with Few Queries
[chapter]

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We consider a

doi:10.1137/1.9781611975031.21
dblp:conf/soda/YamaguchiM18
fatcat:ltoocexiive3xfixxyiuu7n6x4
*stochastic*variant of the packing-type*integer*linear*programming*problem, which contains random variables in the objective vector. ... We also demonstrate our framework by applying it to a variety of*stochastic*combinatorial optimization problems such as matching, matroid, and stable set problems. * This is the final draft of an accepted ... Other variants of the*stochastic*packing*integer**programming*problem with queries have been studied. ...##
###
Mixed-Integer Value Functions in Stochastic Programming
[chapter]

2003
*
Lecture Notes in Computer Science
*

##
###
Fenchel decomposition for stochastic mixed-integer programming

2011
*
Journal of Global Optimization
*

This paper introduces a new cutting plane method for two-stage

doi:10.1007/s10898-011-9817-8
fatcat:kfcxuqv5vvgzvmdzvycv3n7s6i
*stochastic*mixed-*integer**programming*(SMIP) called Fenchel decomposition (FD). ... FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from*integer**programming*. ... A finite branchand-bound algorithm for devised by Ahmed et al. (2004) considers two-stage*stochastic**integer**programs*with general*integer*first-stage. ...
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