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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Convexity and Optimization in Finite Dimensions I (Paperback, Softcover reprint of the original 1st ed. 1970)
Loot Price: R2,632
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Convexity and Optimization in Finite Dimensions I (Paperback, Softcover reprint of the original 1st ed. 1970)
Series: Grundlehren der mathematischen Wissenschaften, 163
Expected to ship within 10 - 15 working days
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Dantzig's development of linear programming into one of the most
applicable optimization techniques has spread interest in the
algebra of linear inequalities, the geometry of polyhedra, the
topology of convex sets, and the analysis of convex functions. It
is the goal of this volume to provide a synopsis of these topics,
and thereby the theoretical back ground for the arithmetic of
convex optimization to be treated in a sub sequent volume. The
exposition of each chapter is essentially independent, and attempts
to reflect a specific style of mathematical reasoning. The emphasis
lies on linear and convex duality theory, as initiated by Gale,
Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the
theoretical development whose impact on modern optimi zation
techniques has been the most pronounced. Chapters 5 and 6 are
devoted to two characteristic aspects of duality theory: conjugate
functions or polarity on the one hand, and saddle points on the
other. The Farkas lemma on linear inequalities and its
generalizations, Motzkin's description of polyhedra, Minkowski's
supporting plane theorem are indispensable elementary tools which
are contained in chapters 1, 2 and 3, respectively. The treatment
of extremal properties of polyhedra as well as of general convex
sets is based on the far reaching work of Klee. Chapter 2
terminates with a description of Gale diagrams, a recently
developed successful technique for exploring polyhedral
structures."
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