1. CMB 2011 (vol 55 pp. 697)
|Constructions of Uniformly Convex Functions|
We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.
Keywords:convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, norm
Categories:52A41, 46G05, 46N10, 49J50, 90C25
2. CMB 2003 (vol 46 pp. 575)
|Optimization of Polynomial Functions |
This paper develops a refinement of Lasserre's algorithm for optimizing a polynomial on a basic closed semialgebraic set via semidefinite programming and addresses an open question concerning the duality gap. It is shown that, under certain natural stability assumptions, the problem of optimization on a basic closed set reduces to the compact case.
Categories:14P10, 46L05, 90C22
3. CMB 2000 (vol 43 pp. 25)
|Subdifferential Regularity of Directionally Lipschitzian Functions |
Formulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established.
Keywords:subdifferential regularity, directional regularity, directionally Lipschitzian functions
Categories:49J52, 58C20, 49J50, 90C26