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An Adjustable Robust Two-stage Stochastic Quadric Programming and its Solution with Subgradient Algorithms

Published: 30 January 2023 Publication History

Abstract

Robust stochastic optimization provides a worst-case decision-making scheme under uncertain probability distributions, but the results could be too conservative and pessimistic. This paper establishes a class of adjustable robust two-stage stochastic quadratic programming based on a parameter-related affine uncertain set. The convexity of the problem is verified, and the subdifferential is obtained. An improved subgradient algorithm is proposed for solving the problem based on a deflected subgradient direction and a step-size strategy with exponential decay. The convergence of the algorithm is proved, and the numerical examples demonstrate the effectiveness. The calculation results show that the adjustable robust stochastic programming is related to the parameter-related, and the optima value decreases as the parameter increases. The approach can provide decision-makers with more optimistic solutions besides the worst-case ones.

References

[1]
John R. Birge and François Louveaux. 2011. Introduction to Stochastic Programming. Springer New York, New York, NY.
[2]
Herbert Scarf. 2005. A Min-Max Solution of an Inventory Problem. In Herbert Scarf's Contributions to Economics, Game Theory and Operations Research, Zaifu Yang (ed.). Palgrave Macmillan UK, London, 19–27.
[3]
Fouad. Ben Abdelaziz and Hatem Masri. 2005. Stochastic programming with fuzzy linear partial information on probability distribution. European Journal of Operational Research 162, 3 (May 2005), 619–629.
[4]
Fouad Ben Abdelaziz and Hatem Masri. 2009. Multistage stochastic programming with fuzzy probability distribution. Fuzzy Sets and Systems 160, 22 (November 2009), 3239–3249.
[5]
Dimitris Bertsimas, Vineet Goyal, and Brian Y. Lu. 2015. A tight characterization of the performance of static solutions in two-stage adjustable robust linear optimization. Math. Program. 150, 2 (May 2015), 281–319.
[6]
Erick Delage and Yinyu Ye. 2010. Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems. Operations Research 58, 3 (June 2010), 595–612.
[7]
Huifu Xu, Yongchao Liu, and Hailin Sun. 2018. Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods. Math. Program. 169, 2 (June 2018), 489–529.
[8]
Arash Gourtani, Tri-Dung Nguyen, and Huifu Xu. 2020. A distributionally robust optimization approach for two-stage facility location problems. EURO Journal on Computational Optimization 8, 2 (June 2020), 141–172.
[9]
A. Ben-Tal, Laurent El Ghaoui, and A. S. Nemirovskiĭ. 2009. Robust optimization. Princeton University Press, Princeton.
[10]
R. T. Rockafellar and R. J.-B. Wets. 1986. A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming. In Stochastic Programming 84 Part II, Andras Prékopa and Roger J.- B. Wets (eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 63–93.
[11]
Xiaojun Chen, Liqun Qi, and Robert S.Womersley 1995. Newton's method for quadratic stochastic programs with recourse. J. Computational and Applied Mathematics 60,1-2(June 1995), 29-46. https://doi.org/10.1016/0377-0427(94)00082-C
[12]
E.Kofler. 2001. Linear partial information with applications. Fuzzy Sets and Systems 118,1(February 2001),167-177. https://doi.org/10.1016/S0165-0114(99)00088-3
[13]
Naum Zuselevich Shor. 1985. Minimization Methods for Non-Differentiable Functions. Springer Berlin Heidelberg, Berlin, Heidelberg.
[14]
Stephen P. Boyd and Lieven Vandenberghe. 2004. Convex optimization. Cambridge University Press, Cambridge, UK ; New York.
[15]
P. M. Camerini, L. Fratta, and F. Maffioli. 1975. On improving relaxation methods by modified gradient techniques. Springer-Verlag Berlin,3(August 1975),26-34. https://doi.org/10.1007/BFb0120697
[16]
Hanif D Sherali, Gyunghyun Choi, and Cihan H Tuncbilek. 2000. A variable target value method for nondi erentiable optimization. Operations Research Letters (2000), 8.
[17]
Rachid Belgacem and Abdessamad Amir. 2018. A new modified deflected subgradient method. Journal of King Saud University - Science 30, 4 (October 2018), 561–567.
[18]
Krzysztof C.Kiwiel. 1986. An aggregate subgradient method for nonsmooth and nonconvex minimization. Journal of Computational and Applied Mathematics 14,3(August 1986).391-400. https://doi.org/10.1016/0377-0427(86)90075-0
[19]
Juhriyansyah Dalle, Dwi Hastuti, and Muhammad Riko Anshori Prasetya. 2021. The use of an application running on the ant colony algorithm in determining the nearest path between two points, Journal of Advances in Information Technology 12,3(August 2021),206-213.
[20]
Khaoula Hassoune, Wafaa Dachry, Fouad Moutaouakkil, and Hicham Medromi. 2020. Dynamic parking guidance architecture using ant colony optimization and multi-agent systems," Journal of Advances in Information Technology 11,2(May 2020),58-63.

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ICACS '22: Proceedings of the 6th International Conference on Algorithms, Computing and Systems
September 2022
132 pages
ISBN:9781450397407
DOI:10.1145/3564982
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 30 January 2023

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Author Tags

  1. Linear partial information
  2. Robust stochastic programming
  3. Subgradient algorithm
  4. Two-stage stochastic programming

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