Bounds are obtained on the minimum for convex and strongly convex functions on convex sets XA nk and XB nk . A theorem on the sufficient condition for a minimum of a convex function on A nk is proved.doi:10.1007/BF01069996S. V. Yakovlev...
functionsmaximum principleminimum principleRadon transformsset theory/ convexificationnonconvex functionsThis note, through discussing convexification of functions on any sets, extends Stegall's maximum principle to nonconvex sets, and generalizes Ghoussoub-Maurey's principle of dual spaces....
The class of quasiconvex functions are not closed under summation, even summing a quasiconvex function with a linear function might not be quasiconvex as shown inthis post. So the Lagrangian function of your problem can have many local minimal and so the KKT conditions can have many solutions ...
isF-subharmonic. This generalises the classical statement that the marginal function of a convex function is again convex. We also prove a complex version of this result that generalises the Kiselman minimum principle for the marginal function of a plurisubharmonic function. Acknowledgements The autho...
2. (d(A i,A j) is the distance between A i and A j) In the following we will show that μ n has itsleast valueonly when the length of each edge equals to min 1≤i≠j≤nd(A i,A j) and its infimum is 15+33, which can be got only when the convex 6-gon degenerate to ...
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The convex hull of these points is then computed using my Convex Hull function, and finally the minimum enclosing circle is ascertained by my Minimum Enclosing Circle function. More information about these functions and the various algorithms used can be found on their respective program pages....
The set of initial conditions is assumed to be a convex polytope. The problem is reduced to devising a control function whose components are bounded functions over a given interval which maps the vertices of the polytope into a closed ball with the center at the origin, and has the least ...
Let \(({\varvec{Z}})_{+}\) be the operator projecting the matrix \({\varvec{Z}}\) onto the convex cone \(\{{\varvec{\Theta }}\succeq \nu {\varvec{I}}\}\), where \(\nu \) is an arbitrarily small positive number. Assuming that the matrix \({\varvec{Z}}\) has ...
In this paper, a one-shot approach for minimum compliance topology optimization is investigated. In the convex case of variable thickness sheet optimizatio