Probabilistic optimization via approximate p-efficient points and bundle methods

作者: W. van Ackooij , V. Berge , W. de Oliveira , C. Sagastizábal

DOI: 10.1016/J.COR.2016.08.002

关键词: MathematicsProbabilistic logicStochastic programmingProbabilistic optimizationDuality (optimization)Bundle methodsMathematical optimization

摘要: For problems when decisions are taken prior to observing the realization of underlying random events, probabilistic constraints an important modeling tool if reliability is a concern. A key concept numerically dealing with that p-efficient points. By adopting dual point view, we develop solution framework includes and extends various existing formulations. The unifying approach built on basis recent generation bundle methods called on-demand accuracy, characterized by its versatility flexibility. Numerical results for several difficult confirm interest approach.

参考文章(64)
A. Prékopa, T. Szántai, Flood control reservoir system design using stochastic programming Mathematical Programming in Use. pp. 138- 151 ,(1978) , 10.1007/BFB0120831
René Henrion, Cyrille Strugarek, Convexity of Chance Constraints with Dependent Random Variables: The Use of Copulae Springer, New York, NY. pp. 427- 439 ,(2011) , 10.1007/978-1-4419-9586-5_17
Claudia A. Sagastizábal, J. Frédéric Bonnans, Claude Lemaréchal, Jean Charles Gilbert, Numerical Optimization: Theoretical and Practical Aspects (Universitext) Springer-Verlag New York, Inc.. ,(2006)
R. T. Rockafellar, R. J.-B. Wets, A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming Mathematical Programming Studies. pp. 63- 93 ,(1986) , 10.1007/BFB0121126
A. Pr�kopa, Dual method for the solution of a one-stage stochastic programming problem with random RHS obeying a discrete probability distribution ZOR Zeitschrift f�r Operations Research Methods and Models of Operations Research. ,vol. 34, pp. 441- 461 ,(1990) , 10.1007/BF01421551
Michael Hintermüller, A Proximal Bundle Method Based on Approximate Subgradients Computational Optimization and Applications. ,vol. 20, pp. 245- 266 ,(2001) , 10.1023/A:1011259017643
Wim van Ackooij, Antonio Frangioni, Milad Tahanan, Fabrizio Lacalandra, Large-scale Unit Commitment under uncertainty: a literature survey Università di Pisa. ,(2014)
Stanislav P. Uryasev, Probabilistic constrained optimization : methodology and applications Kluwer Academic Publishers. ,(2000)