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 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.

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).

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.