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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Convexity and Well-Posed Problems (Paperback, Softcover reprint of hardcover 1st ed. 2006)
Loot Price: R1,476
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Convexity and Well-Posed Problems (Paperback, Softcover reprint of hardcover 1st ed. 2006)
Series: CMS Books in Mathematics
Expected to ship within 10 - 15 working days
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Total price: R1,496
Discovery Miles: 14 960
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This book deals mainly with the study of convex functions and their
behavior from the point of view of stability with respect to
perturbations. We shall consider convex functions from the most
modern point of view: a function is de?ned to be convex whenever
its epigraph, the set of the points lying above the graph, is a
convex set. Thus many of its properties can be seen also as
properties of a certain convex set related to it. Moreover, we
shall consider extended real valued functions, i. e. , functions
taking possibly the values?? and +?. The reason for considering the
value +? is the powerful device of including the constraint set of
a constrained minimum problem into the objective function itself
(by rede?ning it as +? outside the constraint set). Except for
trivial cases, the minimum value must be taken at a point where the
function is not +?, hence at a point in the constraint set. And the
value ?? is allowed because useful operations, such as the
inf-convolution, can give rise to functions valued?? even when the
primitive objects are real valued. Observe that de?ning the
objective function to be +? outside the closed constraint set
preserves lower semicontinuity, which is the pivotal and mi- mal
continuity assumption one needs when dealing with minimum problems.
Variational calculus is usually based on derivatives.
General
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