NDLI: On the convexity of probabilistically constrained linear programs

Content Provider	IEEE Xplore Digital Library
Author	Lagoa, C.M.
Copyright Year	1999
Description	Author affiliation: Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA (Lagoa, C.M.)
Abstract	The focal point of this paper is the so-called Probabilistically Constrained Linear Program (PCLP), also known as Chance Constrained Linear Program. We prove that PCLP is a convex program when the uncertain parameters are uniformly distributed over a convex symmetric set Q. By symmetric we mean that if q/spl isin/Q then -q/spl isin/Q. Furthermore, we provide a deterministic equivalent of the PCLP which, in some cases, leads to an implementation that does not require the use of stochastic programming; only commonly available optimization tools are required. Finally, the concept of Probabilistically Robust Linear Program (PRLP) is introduced. The PRLP is a generalization of the PCLP for the case when the distribution of the uncertain coefficients is not known. The only assumption is that their distribution belongs to a known class /spl Fscr/. Since the true distribution of the uncertain parameters is not available, in the PRLP it is required that the probability of satisfaction of the constraints is greater than a given risk level /spl epsi/ for all possible distributions f/spl isin//spl Fscr/. It is proven that the PRLP is also a convex program for the class /spl Fscr/.
Starting Page	516
Ending Page	521
File Size	508591
Page Count	6
File Format	PDF
ISBN	0780352505
ISSN	01912216
DOI	10.1109/CDC.1999.832834
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-12-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Stochastic processes Robustness Independent component analysis
Content Type	Text
Resource Type	Article

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