In this paper, we discuss 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 the lower bounds of the robustness functions. A ...

We say that the width of an infinite subgroup H in G is n if there exists a collection of n essentially distinct conjugates of H such that the intersection of any two elements of the collection is infinite and n is maximal possible. We define the width of a finite subgroup to be 0. We prove that a quasiconvex subgroup of a negatively curved group has finite width. It follows that geometrically ...

A quasiconvex function f being given, does there exist an increasing and continuous k which makes $$k\circ f$$ convex? How to build such a k? Some words on least convex (concave) functions. The ratio of two positive numbers is neither locally convexifiable nor concavifiable. Finally, some considerations the approximation preorder from finite number observations revealed preference problem are d...

This note proposes to modify the definition of quasiconvexity of a function f Úìm˜n r Ï ñ Ú ̈ ñ T −ðÙð( on the spaceìm˜n of m ˜ n matrices in such a way that (i) the polyconvexity implies quasiconvexity without any additional measurability or continuity assumption on f and (ii) the pointwise supremum of any family of quasiconvex functions is a quasiconvex function. Property (ii) allows one to de...

It is known that any local maximizer of an explicitly quasiconvex realvalued function is actually a global minimizer, whenever it belongs to the intrinsic core of the function’s domain. We show that a similar property holds for componentwise explicitly quasiconvex vector-valued functions, with respect to the optimality concepts of ideal, strong and weak efficiency. These new results are applied...

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...