We prove that quasiconvex functions always admit descent trajectories bypassing all non-minimizing critical points.

A disjunctive programming problem corresponds to the minimization of an objective function on a constraint set which is a union of sets, for example, min f (x) s.t. min j∈ J g j (x) ≤ 0 where the functions f and g j are real valued defined on a Banach space X and J is a (possibly infinite) index set. This class of problems has been introduced by Balas [4] in 1974 and then studied by many author...

This paper discusses evaluation techniques of the robustness function of trusses, which is regarded as one of measures of structural robustness, under the uncertainties of member stiffnesses and external forces. By using quadratic embedding of the uncertainty and the S-procedure, we formulate a quasiconvex optimization problem which provides lower bounds of the robustness functions. A bisection...

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...

In this article we develop a global optimization algorithm for quasiconvex programming where the objective function is a Lipschitz function which may have “flat parts”. We adapt the Extended Cutting Angle method to quasiconvex functions, which reduces significantly the number of iterations and objective function evaluations, and consequently the total computing time. Applications of such an alg...