Entropy Optimization and Mathematical Programming by S.-C. Fang, J. R. Rajasekera, H.-S. J. Tsao (auth.)

By S.-C. Fang, J. R. Rajasekera, H.-S. J. Tsao (auth.)

Entropy optimization is an invaluable blend of classical engineering thought (entropy) with mathematical optimization. The ensuing entropyoptimization models have proved their usefulness with profitable purposes in components similar to photograph reconstruction, trend reputation, statistical inference, queuing thought, 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 varied fields, a great number of acceptable resolution equipment were loosely developed with no 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 components. the aim of this ebook is to fulfill this want. Entropy Optimization andMathematical Programming deals views that meet the desires of numerous user communities in order that the clients can practice entropyoptimization techniques with whole convenience and straightforwardness. With this attention, the authors concentrate on the entropy optimization difficulties in finite dimensional Euclidean area such that just some uncomplicated familiarity with optimization is needed of the reader.

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Extra resources for Entropy Optimization and Mathematical Programming

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Image 42 CHAPTER 2 reconstruction is a procedure for processing the measurement data to construct an image of the object. Readers are referred to [21, 6, 41] and the references therein for detailed descriptions. A very important scientific application of image reconstruction is in computerized tomography (CT) for medical diagnosis. Physicians need to know, for example, the location, shape, and size of a suspected tumor inside a patient's brain in order to plan a suitable course of treatment. With computerized tomography, images of cross-sections of a human body can be constructed from the data obtained by measuring the attenuation of X-rays along a large number of straight lines (or strips) through each cross-section.

Similarly, the term skw in the first constraint can be refined by using s~w to represent the area used by a type w household with a type k house in a zone i. i I - < H'! 80) w where H~ denotes the number of type k houses available in zone i. J ' " 35 = Hi? Vi,k. 81) W Note that Herbert and Stevens' model ignored the spatial interaction between home location and work location. To address this issue, let us assume that every household has only one key worker and the worker works in a particular zone j.

Assume that the measurement data are obtained by observing m projections. We denote the measurement data by d == (d 1 , d 2 , ••• , dm). 117) where A = [aij] is a projection matrix. 117) reflects the possible errors in modeling and measurement. Entropy Optimization Models 43 A number of models have been developed for solving the image reconstruction problem. In this section, we focus on the method that discretizes the image and partition its support into a finite number of equi-sized squared regions (called pixels or cells) whose centers are the n sample points.

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