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Trees and Hills: Methodology for Maximizing Functions of Systems of Linear Relations by Rick Greer d
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Product Details:


Author(s): Rick Greer

Category: Mathematics

Date: 1984

Pages: 366

Publisher: Elsevier Science Ltd

Language: English

ISBN-10: 0444875786

Format: PDF

Book Description:

The tree algorithm described in this monograph is an algorithm which maximizes functions of systems of linear relations subject to constraints. Typical problems in this class are concerned with identifying all of those vectors which satisfy or donвt satisfy given linear equalities or inequalities in such patterns as will maximize certain functions of interest. For example, consider the problem of identifying all of those vectors which satisfy as many of an inconsistent system of linear inequalities as possible. For another example, consider two overlapping multidimensional clouds of 0 в s and xвs; in this setting, the problem is to determine ail quadratic hypersurfaces which best separate the clouds in the sense of having the fewest number of 0 в s on the x side of the surface and vice-versa. Also, as very special cases, this class includes the problems of solving linear programs and systems of linear equations.

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