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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 56, 2007 - Issue 4: Dedicated to the memory of Prof. Dr. František Nožicka, Guest Editors: Bernd Bank, Jürgen Guddat, Horst Hollatz, Hubertus Th. Jongen, Klaus Lommatzsch and Karel Zimmermann
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Original Articles

Structural properties of linear probabilistic constraints

R. Henrion Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, GermanyCorrespondence[email protected]
Pages 425-440 | Received 10 Jul 2005, Accepted 29 Dec 2005, Published online: 27 Oct 2009

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Zhaolin Hu, Wenjie Sun & Shushang Zhu. (2022) Chance constrained programs with Gaussian mixture models. IISE Transactions 54:12, pages 1117-1130.
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Rashed Khanjani Shiraz, Vincent Charles, Madjid Tavana & Debora Di Caprio. (2017) A redundancy detection algorithm for fuzzy stochastic multi-objective linear fractional programming problems. Stochastic Analysis and Applications 35:1, pages 40-62.
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Qingyun He & Chuanyang Hong. (2023) A data-driven robust EVaR-PC with application to portfolio management. PLOS ONE 18:6, pages e0287093.
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V Varagapriya, Vikas Vikram Singh & Abdel Lisser. (2022) Joint chance-constrained Markov decision processes. Annals of Operations Research 322:2, pages 1013-1035.
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Nan Jiang & Weijun Xie. (2022) ALSO-X and ALSO-X+: Better Convex Approximations for Chance Constrained Programs. Operations Research 70:6, pages 3581-3600.
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Ying Cui, Junyi Liu & Jong-Shi Pang. (2022) Nonconvex and Nonsmooth Approaches for Affine Chance-Constrained Stochastic Programs. Set-Valued and Variational Analysis 30:3, pages 1149-1211.
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Shen Peng, Francesca Maggioni & Abdel Lisser. (2022) Bounds for probabilistic programming with application to a blend planning problem. European Journal of Operational Research 297:3, pages 964-976.
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Shen Peng, Abdel Lisser, Vikas Vikram Singh, Nalin Gupta & Eshan Balachandar. (2021) Games with distributionally robust joint chance constraints. Optimization Letters 15:6, pages 1931-1953.
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Shen Peng, Navnit Yadav, Abdel Lisser & Vikas Vikram Singh. (2021) Chance-constrained games with mixture distributions. Mathematical Methods of Operations Research 94:1, pages 71-97.
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Vikas Vikram Singh, Abdel Lisser & Monika Arora. (2021) An equivalent mathematical program for games with random constraints. Statistics & Probability Letters 174, pages 109092.
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Jean B. Lasserre & Tillmann Weisser. (2019) Distributionally robust polynomial chance-constraints under mixture ambiguity sets. Mathematical Programming 185:1-2, pages 409-453.
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Zhiping Chen, Shen Peng & Abdel Lisser. (2020) A sparse chance constrained portfolio selection model with multiple constraints. Journal of Global Optimization 77:4, pages 825-852.
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Alejandra Peña-Ordieres, James R. Luedtke & Andreas Wächter. (2020) Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation. SIAM Journal on Optimization 30:3, pages 2221-2250.
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Alejandra Pena-Ordieres, Daniel K Molzahn, Line Roald & Andreas Waechter. (2020) DC Optimal Power Flow with Joint Chance Constraints. IEEE Transactions on Power Systems, pages 1-1.
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S. N. Vasil’eva & Yu. S. Kan. (2019) Approximation of Probabilistic Constraints in Stochastic Programming Problems with a Probability Measure Kernel. Automation and Remote Control 80:11, pages 2005-2016.
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Vikas Vikram Singh & Abdel Lisser. (2019) A second-order cone programming formulation for two player zero-sum games with chance constraints. European Journal of Operational Research 275:3, pages 839-845.
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Yuri S. Kan & Sofia N. Vasil’eva. 2019. Mathematical Optimization Theory and Operations Research. Mathematical Optimization Theory and Operations Research 497 507 .
Vikas Vikram Singh & Abdel Lisser. (2018) Variational inequality formulation for the games with random payoffs. Journal of Global Optimization 72:4, pages 743-760.
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Ming Zhao, Kai Huang & Bo Zeng. (2016) A polyhedral study on chance constrained program with random right-hand side. Mathematical Programming 166:1-2, pages 19-64.
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Jean B. Lasserre. (2017) Representation of Chance-Constraints With Strong Asymptotic Guarantees. IEEE Control Systems Letters 1:1, pages 50-55.
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Xiaojin Zheng, Baiyi Wu & Xueting Cui. (2017) Cell-and-bound algorithm for chance constrained programs with discrete distributions. European Journal of Operational Research 260:2, pages 421-431.
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Andre Luiz Diniz & René Henrion. (2015) On probabilistic constraints with multivariate truncated Gaussian and lognormal distributions. Energy Systems 8:1, pages 149-167.
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Miles Lubin, Yury Dvorkin & Scott Backhaus. (2016) A Robust Approach to Chance Constrained Optimal Power Flow With Renewable Generation. IEEE Transactions on Power Systems 31:5, pages 3840-3849.
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Vikas Vikram Singh, Oualid Jouini & Abdel Lisser. (2016) Existence of Nash equilibrium for chance-constrained games. Operations Research Letters 44:5, pages 640-644.
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Michel Minoux & Riadh Zorgati. (2015) Convexity of Gaussian chance constraints and of related probability maximization problems. Computational Statistics 31:1, pages 387-408.
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Alexander Kogan & Miguel A. Lejeune. (2013) Threshold Boolean form for joint probabilistic constraints with random technology matrix. Mathematical Programming 147:1-2, pages 391-427.
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Volker Schulz & Claudia Schillings. 2013. Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics. Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics 297 338 .
Xiaodi Bai, Xiaojin Zheng & Xiaoling Sun. (2012) A survey on probabilistically constrained optimization problems. Numerical Algebra, Control and Optimization 2:4, pages 767-778.
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L. Jeff Hong, Yi Yang & Liwei Zhang. (2011) Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach. Operations Research 59:3, pages 617-630.
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James J. Cochran, Louis A. CoxJr.Jr., Pinar Keskinocak, Jeffrey P. Kharoufeh & J. Cole SmithRené Henrion. 2011. Wiley Encyclopedia of Operations Research and Management Science. Wiley Encyclopedia of Operations Research and Management Science.
Radu Ioan Bot, Nicole Lorenz & Gert Wanka. (2010) DUALITY FOR LINEAR CHANCE-CONSTRAINED OPTIMIZATION PROBLEMS. Journal of the Korean Mathematical Society 47:1, pages 17-28.
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Huanyin Chen. (2010) ON QUASI-STABLE EXCHANGE IDEALS. Journal of the Korean Mathematical Society 47:1, pages 1-15.
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Andreas Eichhorn, Holger Heitsch & Werner Römisch. 2010. Handbook of Power Systems II. Handbook of Power Systems II 405 432 .
Volker Schulz & Claudia Schillings. (2009) Problem Formulations and Treatment of Uncertainties in Aerodynamic Design. AIAA Journal 47:3, pages 646-654.
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René Henrion & Cyrille Strugarek. (2007) Convexity of chance constraints with independent random variables. Computational Optimization and Applications 41:2, pages 263-276.
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Xin Chen, Melvyn Sim, Peng Sun & Jiawei Zhang. (2008) A Linear Decision-Based Approximation Approach to Stochastic Programming. Operations Research 56:2, pages 344-357.
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