maximal elements of sub-topical functions with applications to global optimization

Maximal elements of sub-topical functions with applications to global optimization

We study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

Characterizing sub-topical functions

In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...

Global Optimization of Polynomial Functions and Applications

Global Optimization of Polynomial Functions and Applications by Jiawang Nie Doctor of Philosophy in Applied Mathematics University of California, Berkeley Professor James Demmel, Co-Chair Professor Bernd Sturmfels, Co-Chair This thesis discusses the global optimization problem whose objective function and constraints are all described by (multivariate) polynomials. The motivation is to find the...

Global Optimization of Costly Nonconvex Functions, with Financial Applications

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

Condorcet choice functions and maximal elements

Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Mor...