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Semiiterative minimum crossentropy algorithms for rareevents, counting, combinatorial and integer programming,” Methodology and Computing
 in Applied Probability
, 2008
"... We present a new generic minimum crossentropy method, called the semiiterative MinxEnt, or simply SME, for rareevent probability estimation, counting, and approximation of the optimal solutions of a broad class of NPhard linear integer and combinatorial optimization problems (COP’s). The main i ..."
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We present a new generic minimum crossentropy method, called the semiiterative MinxEnt, or simply SME, for rareevent probability estimation, counting, and approximation of the optimal solutions of a broad class of NPhard linear integer and combinatorial optimization problems (COP’s). The main idea of our approach is to associate with each original problem an auxiliary singleconstrained convex MinxEnt program of a special type, which has a closedform solution. We prove that the optimal pdf obtained from the solution of such a specially designed MinxEnt program is a zero variance pdf, provided the “temperature ” parameter is set to minus infinity. In addition we prove that the parametric pdf based on the product of marginals obtained from the optimal zero variance pdf coincides with the parametric pdf of the standard crossentropy (CE) method. Thus, originally designed at the end of 1990s as a heuristics for estimation of rareevents and COP’s, CE has strong connection with MinxEnt, and thus, strong mathematical foundation.
A STOCHASTIC OPTIMIZATION METHOD FOR PARTIALLY DECOMPOSABLE PROBLEMS, WITH APPLICATION TO ANALYSIS OF NMR SPECTRA
"... and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication an ..."
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and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission.