We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixedinteger sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary pol...

We consider approximations of a smooth convex body by inscribed and circumscribed convex polytopes as the number of vertices, resp. facets tends to innnity. The measure of deviation used is the diierence of the mean width of the convex body and the approximating polytopes. The following results are obtained. (i) An asymptotic formula for best approximation. (ii) Upper and lower estimates for st...

We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given close to one probability, a system of randomly perturbed convex constraints. Our goal is to build a computationally tractable approximation of this (typically intractable) problem, i.e., an explicitly given deterministic optimization program with the feasible set cont...

This paper proposes an initialization approach for parameter estimation problems (PEPs) involving parameter-affine dynamic models. By using the state measurements, the nonconvex PEP is modified such that a convex approximation to the original PEP is obtained. The modified problem is solved by vailable online 5 November 2009 eywords: arameter estimation ultiple shooting onvex optimization convex...

This letter considers the weighted sum-rate maximization (WSRMax) problem in downlink multicell multiuser orthogonal frequency-division multiplexing system. The WSRMax problem under per base station transmit power constraint is known to be NP-hard, and the optimal solution is computationally very expensive. We propose two lesscomplex suboptimal convex approximated solutions which are based on s...