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."

A performance of Alban Berg's opera recorded at the Salzburg Festival in 2011. The opera, dark and satirical in tone, charts the story of the rise and fall of a femme fatale, from life as a society hostess to prostitution and, eventually, a bloody death at the hands of Jack the Ripper. French soprano Patricia Petibon heads a strong European cast, while German conductor Marc Albrecht leads the Wiener Philharmoniker.

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."

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.

Daniele Gatti conducts the Wiener Philharmoniker and Konzertvereinigung Wiener Staatsopernchor in this production of Wagner's opera, recorded at the 2013 Salzburg Festival. The cast includes Michael Volle, Roberto Saccà, Georg Zeppenfeld and Monika Bohinec.

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.

Jens Neubert directs this filmed version of Carl Maria von Weber's romantic opera 'Der Freischütz', (The Marksman). The story follows Max (Michael König) and Kasper (Michael Volle), two hunters who, as well as fighting alongside each other in the Napoleonic Wars, are vying for the love of the beautiful Agathe (Juliane Banse).

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.