Two-stage quadratic integer programs with stochastic right-hand sides

Özaltın, Osman Y.; Prokopyev, Oleg A.; Schaefer, Andrew J.

doi:10.1007/s10107-010-0412-4

Cited by 16 publications

(3 citation statements)

References 57 publications

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“…As demonstrated in the previous work in the literature (see, e.g., somewhat related PI's work in [9] funded by an earlier grant from AFOSR), one of the main advantages of such approaches is their relative insensitivity to the number of variables and scenarios. However, this comes at the price of sensitivity to both the number of constraints in each stage and the magnitude of right-hand sides because of value function storage requirements.…”

Section: Solving Stochastic Ips and Mipsmentioning

confidence: 99%

New Theory and Methods in Stochastic Mixed Integer Programming

Prokopyev¹

2014

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Section: Solving Stochastic Ips and Mipsmentioning

confidence: 99%

New Theory and Methods in Stochastic Mixed Integer Programming

Prokopyev¹

2014

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“…Another special case of TSS-CMIP is two-stage stochastic convex quadratic integer program (TSS-QIP). Özaltin et al [45] study TSS-QIPs with only stochastic right-hand sides in the second stage along with deterministic quadratic objective functions, linear constraints, and only integer variables in both stages. They reformulate this problem using value functions for quadratic integer programs, and present a global branch-and-bound algorithm and a level-set approach to solve the problem.…”

Section: Literature Review On Special Cases Of Tss-cmip and Tsdr-cmipmentioning

confidence: 99%

Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs

Bansal

Zhang

2021

J Glob Optim

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In this paper, we derive (partial) convex hull for deterministic multi-constraint polyhedral conic mixed integer sets with multiple integer variables using conic mixed integer rounding (CMIR) cut-generation procedure of Atamtürk and Narayanan (Math Prog 122:1-20, 2008), thereby extending their result for a simple polyhedral conic mixed integer set with single constraint and one integer variable. We then introduce two-stage stochastic p-order conic mixed integer programs (denoted by TSS-CMIPs) in which the second stage problems have sum of l p -norms in the objective function along with integer variables. First, we present sufficient conditions under which the addition of scenario-based nonlinear cuts in the extensive formulation of TSS-CMIPs is sufficient to relax the integrality restrictions on the second stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We utilize scenario-based CMIR cuts for TSS-CMIPs and their distributionally robust generalizations with structured CMIPs in the second stage, and prove that these cuts provide conic/linear programming equivalent or approximation for the second stage CMIPs. We also perform extensive computational experiments by solving stochastic and distributionally robust capacitated facility location problem and randomly generated structured TSS-CMIPs with polyhedral CMIPs and second-order CMIPs in the second stage, i.e. p = 1 and p = 2, respectively. We observe that there is a significant reduction in the total time taken to solve these problems after adding the scenario-based cuts. KeywordsTwo-stage stochastic p-order conic mixed integer program • Scenario-based cutting planes • Two-stage distributionally robust program • (Partial) convex hull • Conic mixed integer rounding • Multi-module capacitated facility location B Manish Bansal

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“…[12] provide an algorithm for constructing value functions for MIPs. Value functions have also been incorporated into solution approaches for two-stage stochastic integer programs [1,8,11,14]. Various value function approaches have also been applied to the solution of mixed-integer bilevel programs.…”

Section: (Ip(β))mentioning

confidence: 99%

A Gilmore-Gomory-Type Construction of Integer Programming Value Functions

Brown¹,

Zhang²,

Ajayi³

et al. 2020

Preprint

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In this paper, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. In particular, we use a Gilmore-Gomory-type approach to construct IP value functions over a restricted set of variables. We introduce the notion of maximally-contiguous subsets of level sets -volumes in which changes to the constraint right-hand side have no effect on the value function -and relate these structures to IP value functions and optimal solutions.

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Two-stage quadratic integer programs with stochastic right-hand sides

Cited by 16 publications

References 57 publications

New Theory and Methods in Stochastic Mixed Integer Programming

New Theory and Methods in Stochastic Mixed Integer Programming

Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs

A Gilmore-Gomory-Type Construction of Integer Programming Value Functions

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