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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Hardcover)
Loot Price: R2,520
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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Hardcover)
Series: Applied Optimization, v. 40
Expected to ship within 12 - 17 working days
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The main purpose of this book is to present, in a unified approach,
several algorithms for fixed point computation, convex feasibility
and convex optimization in infinite dimensional Banach spaces, and
for problems involving, eventually, infinitely many constraints.
For instance, methods like the simultaneous projection algorithm
for feasibility, the proximal point algorithm and the augmented
Lagrangian algorithm are rigorously formulated and analyzed in this
general setting and shown to be applicable to much wider classes of
problems than previously known. For this purpose, a new basic
concept, "total convexity", is introduced. Its properties are
deeply explored, and a comprehensive theory is presented, bringing
together previously unrelated ideas from Banach space geometry,
finite dimensional convex optimization and functional analysis. For
making a general approach possible the work aims to improve upon
classical results like the Holder-Minkowsky inequality of p. This
book should be of interest to both researchers in nonlinear
analysis and to applied mathematicians dealing with numerical
solution of integral equations, equilibrium problems, image
reconstruction, and optimal control.
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