Mehdi Ghasemi
Lower bounds for polynomials using geometric programming.
Fri, 06/10/2011 - 15:01 — SomNambulAuthors: Mehdi Ghasemi, Murray Marshall
Subjects: Optimization and Control
AbstractWe make use of a result of Hurwitz and Reznick, and a consequence of this
result due to Fidalgo and Kovacec, to determine a new sufficient condition for
a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of
squares. This result generalizes a result of Lasserre and a result of Fidalgo
and Kovacec, and it also generalizes the improvements of these results given in
[6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we
explain how $f_{gp}$ can be computed using geometric programming.The Moment Problem for Continuous Positive Semidefinite Linear functionals.
Fri, 10/15/2010 - 15:01 — SomNambulAuthors: Mehdi Ghasemi, Salma Kuhlmann, Ebrahim Samei
Subjects: Algebraic Geometry
AbstractLet $V$ be the countable dimensional polynomial $\reals$-algebra
$\rx:=\reals[X_1,\...,X_n]$. Let $\tau$ be a locally convex topology on V. Let
$K$ be a closed subset of $\reals^n$, and let $M:=M_{\{g_1, \... g_s\}}$ be a
finitely generated quadratic module in $V$. We investigate the following
question: When is the cone $\Pos(K)$ (of polynomials nonnegative on $K$)
included in the closure of $M$? We give an interpretation of this inclusion
with respect to representing continuous linear functionals by measures.
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