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Quasiconvex Optimization and Location Theory (Hardcover, 1998 ed.)
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Quasiconvex Optimization and Location Theory (Hardcover, 1998 ed.)
Series: Applied Optimization, 9
Expected to ship within 12 - 17 working days
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grams of which the objective is given by the ratio of a convex by a
positive (over a convex domain) concave function. As observed by
Sniedovich (Ref. [102, 103]) most of the properties of fractional
pro grams could be found in other programs, given that the
objective function could be written as a particular composition of
functions. He called this new field C programming, standing for
composite concave programming. In his seminal book on dynamic
programming (Ref. [104]), Sniedovich shows how the study of such
com positions can help tackling non-separable dynamic programs that
otherwise would defeat solution. Barros and Frenk (Ref. [9])
developed a cutting plane algorithm capable of optimizing
C-programs. More recently, this algorithm has been used by
Carrizosa and Plastria to solve a global optimization problem in
facility location (Ref. [16]). The distinction between global
optimization problems (Ref. [54]) and generalized convex problems
can sometimes be hard to establish. That is exactly the reason why
so much effort has been placed into finding an exhaustive
classification of the different weak forms of convexity,
establishing a new definition just to satisfy some desirable
property in the most general way possible. This book does not aim
at all the subtleties of the different generalizations of
convexity, but concentrates on the most general of them all,
quasiconvex programming. Chapter 5 shows clearly where the real
difficulties appear.
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