Generalized Convexity

Generalizations of the classical concept of a convex function have been proposed in various fields such as economics, management science, engineering, statistics and applied sciences during the second half of this century. In addition to new results in more established areas of generalized convexity, this book presents several important developments in recently emerging areas. Also, a number of interesting applications are reported.

Contenu

I. Generalized convex functions.- Univex sets, functions and univex nonlinear programming.- Optimization on closely convex sets.- A note on ordinal concavity.- Generalized concavity in cooperative game theory: characterizations in terms of the core.- On the existence of Nash-equilibrium in n-person generalized concave games.- A deep cut ellipsoid algorithm and quasiconvex programming.- Quasiconvexity and related properties in the calculus of variations.- Ray-quasiconvex and f-quasiconvex functions.- Geodesic convexity on ?n.- A class of differentiable generalized convex functions.- Equivalence between generalized gradients and subdifferentials (lower semigradients) for a suitable class of lower semicontinuous functions.- II. Optimality and duality.- Generalizing convexity for second order optimality conditions.- Regularity conditions for constrained extremum problems via image space approach: the linear case.- Duality theory for convex/quasiconvex functions and its application to optimization.- First order generalized optimality conditions for programming problems with a set constraint.- Abstract nonsmooth nonconvex programming.- A survey on optimality and duality in nonsmooth programming.- III. Generalized monotone maps.- Generalized monotonicity - a survey.- Orderings, generalized convexity and monotonicity.- Generalized monotonicity in non-smooth analysis.- Some invariance properties of generalized monotonicity.- IV. Fractional programming.- On quasiconvexity in fractional programming.- A class of non-linear programs: theoretical and algorithmical results.- Post-buckling analysis of frames by a hybrid path-following method.- Fractional programming under uncertainty.- V. Multiobjective programming.- Generalized concavity and optimality conditions in vector and scalar optimization.- Duality for vector valued B-invex programming.- A cutting plane algorithm for linear optimization over the efficient set.- Multiobjective scheduling problems.- On the relationships between bicriteria problems and non-linear programming.- Contributing authors.