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A function is convex if its epigraph is convex. This geometrical
structure has very strong implications in terms of continuity and
differentiability. Separation theorems lead to optimality
conditions and duality for convex problems. A function is
quasiconvex if its lower level sets are convex. Here again, the geo
metrical structure of the level sets implies some continuity and
differentiability properties for quasiconvex functions. Optimality
conditions and duality can be derived for optimization problems
involving such functions as well. Over a period of about fifty
years, quasiconvex and other generalized convex functions have been
considered in a variety of fields including economies, man agement
science, engineering, probability and applied sciences in
accordance with the need of particular applications. During the
last twenty-five years, an increase of research activities in this
field has been witnessed. More recently generalized monotonicity of
maps has been studied. It relates to generalized convexity off
unctions as monotonicity relates to convexity. Generalized
monotonicity plays a role in variational inequality problems,
complementarity problems and more generally, in equilibrium prob
lems."
Simone Young leads the Bayerisches Staatsorchester in this
production of Pfitzner's opera, directed for the stage by Christian
Stuckl. Performers include Christopher Ventris, Peter Rose, Michael
Volle and Falk Struckmann.
A function is convex if its epigraph is convex. This geometrical
structure has very strong implications in terms of continuity and
differentiability. Separation theorems lead to optimality
conditions and duality for convex problems. A function is
quasiconvex if its lower level sets are convex. Here again, the geo
metrical structure of the level sets implies some continuity and
differentiability properties for quasiconvex functions. Optimality
conditions and duality can be derived for optimization problems
involving such functions as well. Over a period of about fifty
years, quasiconvex and other generalized convex functions have been
considered in a variety of fields including economies, man agement
science, engineering, probability and applied sciences in
accordance with the need of particular applications. During the
last twenty-five years, an increase of research activities in this
field has been witnessed. More recently generalized monotonicity of
maps has been studied. It relates to generalized convexity off
unctions as monotonicity relates to convexity. Generalized
monotonicity plays a role in variational inequality problems,
complementarity problems and more generally, in equilibrium prob
lems."
Franz Welser-Möst conducts the Orchestra and Chorus of the Zurich
Opera House in this performance of Johann Strauss's work filmed in
2001. David Poutney directs with Martin Zysset in the title role
and the cast including Michael Volle, Elizabeth Magnuson and Piotr
Beczala.
A production of Debussy's opera featuring the orchestra and chorus
of the Zurich Opera House, conducted by Franz Welser-Möst. Recorded
in 2004, performers include Rodney Gilfry, Isabel Rey, Michael
Volle and László Polgár.
Christoph von Dohnanyi conducts the Zurich Opera House Orchestra in
this live recording of Richard Strauss's opera from 2006.
Performers include American soprano Emily Magee, Elena Mosuc, and
Italian tenor Roberto Saccà.
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