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On the Use of Copulas in Joint Chance-constrained Programming
Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems, 2014In this paper, we investigate the problem of linear joint probabilistic constraints with normally distributed constraints. We assume that the rows of the constraint matrix are dependent, the dependence is driven by a convenient Archimedean copula. We describe main properties of the problem and show how dependence modeled through copulas translates to ...
Michal Houda, Abdel Lisser
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Archimedean Copulas in Joint Chance-Constrained Programming
2015We investigate the problem of linear joint probabilistic constraints with normally distributed constraints in this paper. We assume that the rows of the constraint matrix are dependent, the dependence is driven by a convenient Archimedean copula. We describe main properties of the problem, show how dependence modeled through copulas translates to the ...
Michal Houda, Abdel Lisser
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Joint Randomized Decisions in Chance-Constrained Programming
Journal of the Operational Research Society, 1984Summary: \textit{S. P. Mukherjee} [ibid. 31, 1045-1047 (1980; Zbl 0441.90078)] has considered the problem (P) of minimizing \(E[X_ 1+X_ 2)\) subject to \[ \Pr ob(\frac{X_ 1}{9}+X_ 2\geq b_ 1,\quad \frac{X_ 2}{9}+X_ 1\geq b_ 2)=\frac{1}{8};\quad X_ 1\geq 0,\quad X_ 2\geq 0, \] where \(b_ 1\) is uniform over (0,2), and \(b_ 2\) is uniform over (0,4 ...
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A split-bernstein approach to chance constrained programs
53rd IEEE Conference on Decision and Control, 2014This paper presents a new computationally scalable framework for accurate solution of chance constrained programs. A Bernstein approximation is used to transcribe the chance constraint into a deterministic constraint, relying heavily upon the evaluation of exponential moment generating functions.
Zinan Zhao, Mrinal Kumar 0002
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A heuristic algorithm for a chance constrained stochastic program
European Journal of Operational Research, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Concetta A. DePaolo, David J. Rader Jr.
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Chance-Constrained Programming Model
2013Chance-constrained programming provides a powerful means of modeling decision systems on the assumption that the constraints will hold at least α of time, where α is the confidence level provided as an approximate safety margin by the decision-maker. For fuzzy decision problems, Liu and Iwamura introduced a maximax chance-constrained programming model,
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On Chance Constrained Programming Problems with Joint Constraints
Management Science, 1973In this paper we consider chance constrained programming problems with joint constraints shown in the literature to be equivalent deterministic nonlinear programming problems. Since most existing computational methods for solution require that the constraints of the equivalent deterministic problem be concave, we obtain a simple condition for which ...
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Fuzzy Chance-Constrained Programming
2002Analogous to stochastic chance-constrained programming (CCP), fuzzy CCP provides a means of allowing the decision-maker to consider objectives and constraints in terms of the possibility of their attainment.
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On Accurate Linear Approximations for Chance-Constrained Programming
Journal of the Operational Research Society, 1988This paper introduces the CHAPS (chance-constrained programming system) algorithm, which uses linearization techniques but gives more accurate solutions than earlier, similar methods.
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A Smoothing Function Approach to Joint Chance-Constrained Programs
Journal of Optimization Theory and Applications, 2014An algorithm for stochastic joint chance-constrained optimization problems is developed using the approximation of probability and constraint functions by a difference of two convex functions. The novelty of the proposed algorithm is in the constructed approximation where the approximats are selected from a class of smoothing functions. The convergence
Feng Shan, Liwei Zhang, Xiantao Xiao
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