8 research outputs found
Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints
Altres ajuts: Australian Research Council DP140103213We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex sets defined by non necessarily convex functions, in terms of tangential subdifferentials. Our main result unifies a recent KKT type theorem obtained by Lasserre for differentiable functions with a nonsmooth version due to Dutta and Lalitha
A mean value theorem for tangentially convex functions
Altres ajuts: acords transformatius de la UABThe main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexit
Well-Behavior, Well-Posedness and Nonsmooth Analysis
AMS subject classification: 90C30, 90C33.We survey the relationships between well-posedness and well-behavior. The latter
notion means that any critical sequence (xn) of a lower semicontinuous function
f on a Banach space is minimizing. Here “critical” means that the remoteness of
the subdifferential ∂f(xn) of f at xn (i.e. the distance of 0 to ∂f(xn)) converges
to 0. The objective function f is not supposed to be convex or smooth and the
subdifferential ∂ is not necessarily the usual Fenchel subdifferential. We are thus
led to deal with conditions ensuring that a growth property of the subdifferential
(or the derivative) of a function implies a growth property of the function itself.
Both qualitative questions and quantitative results are considered
Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints
We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex sets defined by non necessarily convex functions, in terms of tangential subdifferentials. Our main result unifies a recent KKT type theorem obtained by Lasserre for differentiable functions with a nonsmooth version due to Dutta and Lalitha