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Stochastic Integer Programming [chapter]

Leen Stougie
1992 Operations Research Proceedings 1991  
Polynomial time approximation algorithms and their performance guarantees for 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 .  ... 
doi:10.1007/978-3-642-46773-8_100 fatcat:nu2euvyzfre6tfvqt2dkxk2xy4

Stochastic Integer Programming [chapter]

A. R. Kan, L. Stougie
1988 Springer Series in Computational Mathematics  
Polynomial time approximation algorithms and their performance guarantees for 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 .  ... 
doi:10.1007/978-3-642-61370-8_8 fatcat:k46jjqnrbzdp5iua7s4dgfdkse

Stochastic Integer Programming [chapter]

François V. Louveaux, Rüdiger Schultz
2003 Handbooks in Operations Research and Management Science  
doi:10.1016/s0927-0507(03)10004-7 fatcat:cfojzjgyljeihp5mycplgawzjq

Stochastic Integer Programming by Dynamic Programming [chapter]

B. J. Lageweg, J. K. Lenstra, A. R. Kan, L. Stougie
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.  ... 
doi:10.1007/978-3-642-61370-8_21 fatcat:zfmwjqpblvahhmlz2dkiypdvge

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

Shixuan Zhang, Xu Andy Sun
2022 arXiv   pre-print
In this paper, we study multistage 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  ... 
arXiv:1912.13278v5 fatcat:ylpflyescbbx7dmavgedppdk3e

Stochastic Packing Integer Programs with Few Queries [article]

Takanori Maehara, Yutaro Yamaguchi
2019 arXiv   pre-print
We consider a 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.  ... 
arXiv:1707.04020v3 fatcat:myc72wakm5cnxovi35pp7ajoru

Integer Set Reduction for Stochastic Mixed-Integer Programming [article]

Saravanan Venkatachalam, Lewis Ntaimo
2016 arXiv   pre-print
Two-stage 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.  ... 
arXiv:1605.05194v1 fatcat:nfwy2ccip5aszmqaclvopmww2e

Integer programming for weakly coupled stochastic dynamic programs with partial information [article]

Victor Cohen, Axel Parmentier
2020 arXiv   pre-print
Partially observable Markov decision processes (POMDPs) have been introduced to deal with the first challenge, while weakly coupled 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.  ... 
arXiv:2012.00645v4 fatcat:btskg7jdt5gipl32t26ct4kes4

Stochastic programming with simple integer recourse

François V. Louveaux, Maarten H. van der Vlerk
1993 Mathematical programming  
In this paper, we introduce the class of 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 + .  ... 
doi:10.1007/bf01582153 fatcat:2rhuhi5skrgythfd7vrmno2w3u

Finiteness theorems in stochastic integer programming [article]

Matthias Aschenbrenner, Raymond Hemmecke
2005 arXiv   pre-print
We study Graver test sets for families of linear multi-stage 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.  ... 
arXiv:math/0502078v1 fatcat:ff4vawhxobd7lbn3wlu2ooy4vq

Finiteness Theorems in Stochastic Integer Programming

Matthias Aschenbrenner, Raymond Hemmecke
2006 Foundations of Computational Mathematics  
We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios.  ...  Building Blocks In this section we study multistage stochastic integer programs.  ...  integer program.  ... 
doi:10.1007/s10208-005-0174-1 fatcat:r7hbpf32z5h5zkzaa6oc4b6sqy

On Generating Lagrangian Cuts for Two-Stage Stochastic Integer Programs [article]

Rui Chen, James Luedtke
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.  ... 
arXiv:2106.04023v2 fatcat:ta7hu6dowfht5ib5gjppwyjgd4

Stochastic Packing Integer Programs with Few Queries [chapter]

Yutaro Yamaguchi, Takanori Maehara
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We consider a 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.  ... 
doi:10.1137/1.9781611975031.21 dblp:conf/soda/YamaguchiM18 fatcat:ltoocexiive3xfixxyiuu7n6x4

Mixed-Integer Value Functions in Stochastic Programming [chapter]

Rüdiger Schultz
2003 Lecture Notes in Computer Science  
doi:10.1007/3-540-36478-1_16 fatcat:mvwj3blkdncfzg3ll3pv4qt4xm

Fenchel decomposition for stochastic mixed-integer programming

Lewis Ntaimo
2011 Journal of Global Optimization  
This paper introduces a new cutting plane method for two-stage 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.  ... 
doi:10.1007/s10898-011-9817-8 fatcat:kfcxuqv5vvgzvmdzvycv3n7s6i
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