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Recent Developments in Well-Posed Variational Problems (Hardcover, 1995 ed.)
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Recent Developments in Well-Posed Variational Problems (Hardcover, 1995 ed.)
Series: Mathematics and Its Applications, 331
Expected to ship within 10 - 15 working days
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This volume contains several surveys focused on the ideas of
approximate solutions, well-posedness and stability of problems in
scalar and vector optimization, game theory and calculus of
variations. These concepts are of particular interest in many
fields of mathematics. The idea of stability goes back at least to
J. Hadamard who introduced it in the setting of differential
equations; the concept of well-posedness for minimum problems is
more recent (the mid-sixties) and originates with A.N. Tykhonov. It
turns out that there are connections between the two properties in
the sense that a well-posed problem which, at least in principle,
is "easy to solve," has a solution set that does not vary too much
under perturbation of the data of the problem, i.e. it is "stable."
These themes have been studied in depth for minimum problems and
now we have a general picture of the related phenomena in this
case. But, of course, the same concepts can be studied in other
more complicated situations as, e.g. vector optimization, game
theory and variational inequalities. Let us mention that in several
of these new areas there is not even a unique idea of what should
be called approximate solution, and the latter is at the basis of
the definition of well posed problem."
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