NDLI: Stochastic approximation over multidimensional discrete sets with applications to inventory systems and admission control of queueing networks

Content Provider	ACM Digital Library
Author	Lim, Eunji
Copyright Year	2012
Abstract	We propose new methods to solve simulation optimization problems over multidimensional discrete sets. The proposed methods are based on extending the objective function from a discrete domain to a continuous domain and applying stochastic approximation to the extended function. The extension of the objective function is constructed as a piecewise linear interpolation of the original objective function over a particular partition of $ℝ^{d}.$ The advantage of the proposed approach lies in that stochastic approximation is applied to the extension, not the original function, over $ℝ^{d},$ so the estimated optimal solution at each iteration of the proposed methods is not restricted to be an integer point. Rather, we are free to approach the optimal solution aggressively by moving toward the direction of the steepest descent, thereby skipping over intervening points, thereby resulting in fast convergence in the early stage of the procedures. We provide a set of sufficient conditions under which the proposed methods guarantee the almost sure (a.s.) convergence to the optimal solution. One of such conditions is the multimodularity or $L^{♮}-convexity$ of the objective function, which arises in various inventory systems and queueing networks with controlled admission. Numerical examples illustrate the effectiveness of the proposed methods in such settings.
Starting Page	1
Ending Page	23
Page Count	23
File Format	PDF
ISSN	10493301
e-ISSN	15581195
DOI	10.1145/2379810.2379812
Volume Number	22
Issue Number	4
Journal	ACM Transactions on Modeling and Computer Simulation (TOMACS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-11-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Simulation-based optimization Discrete optimiztion
Content Type	Text
Resource Type	Article
Subject	Computer Science Applications Modeling and Simulation

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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