By S.-C. Fang, J. R. Rajasekera, H.-S. J. Tsao (auth.)
Entropy optimization is an invaluable mix of classical engineering idea (entropy) with mathematical optimization. The ensuing entropyoptimization models have proved their usefulness with profitable purposes in parts resembling snapshot reconstruction, trend attractiveness, statistical inference, queuing idea, spectral research, statistical mechanics, transportation making plans, city and neighborhood making plans, input-output research, portfolio funding, details research, and linear and nonlinear programming.
whereas entropy optimization has been utilized in assorted fields, a number of acceptable answer equipment were loosely built with out adequate mathematical remedy. a scientific presentation with right mathematical remedy of this fabric is required by way of practitioners and researchers alike in all program parts. the aim of this publication is to satisfy this desire. Entropy Optimization andMathematical Programming deals views that meet the desires of various user communities in order that the clients can follow entropyoptimization techniques with entire convenience and simplicity. With this attention, the authors specialize in the entropy optimization difficulties in finite dimensional Euclidean house such that just some uncomplicated familiarity with optimization is needed of the reader.
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Additional resources for Entropy Optimization and Mathematical Programming
19-28. , "Image Restoration by a Powerful Maximum Entropy Method," Computer Vision, Graphics, and Image Processing, Vol. 23, 1983, pp. 113-128. , "On Some Optimization Techniques in Image Reconstruction," Applied Numerical Mathematics, Vol. 3, 1987, pp. 365-391. W. L. Kelmanson, and B. Korte, Rio de Janeiro, Brazil, April, 1981, pp. 89-103. , "A Maximum Entropy Analysis of the M/G/1 and G/M/1 Queueing System at Equilibrium," Acta Informatica, Vol. 19, 1983, pp. 339-355. , Modern Portfolio Theory and Investment Analysis, 4th Edition, John Wiley, New York, 1991.
9 may take various forms of entropy optimization problems including those with nonlinear constraints. 4 33 REGIONAL PLANNING Regional planning models dealing with locating centers of activities such as shopping areas, residential areas, and work districts have been developed since the 1960's. This section focuses on the estimation and prediction of the distribution of residential activity in urban areas. , ). Wilson's pioneering work in 1970  started using entropy optimization models for regional planning.
JsjXj), i = 1, ... jXj ), j = 1, ... , n. 63). 63) by an iterative procedure. The name RAS originated from the matrix notation given to the n x n diagonal matrices defined as: R = diag[ri], and S = diag[sj]. It can be shown that (, page 310) A = RAoS. 7. More about the RAS algorithm can be found in [35, 30, 3]. 7 provides the so-called point-estimates of the technical coefficients aij, i, j = 1, ... , n. However, in many cases it may be necessary to replace aij by a set of discrete points Y = [Y1, ••.