The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will be also shown how … Read more
In this tutorial we discuss modeling issues in intensity modulated radiation therapy, contrasting the continuous model with the fully-discretized one and considering feasibility formulations versus optimization setups. We review briefly some mathematical optimization techniques for IMRT. These include global optimization, multi-objective optimization, linear and mixed integer programming and projection methods. Citationin: J.R. Palta and T.R. … Read more
The Morse potential is a simple model pair potential that has a single parameter $\rho$ which determines the width of the potential well and allows a wide variety of materials to be modelled. Morse clusters provide a particularly tough test system for global optimization algorithms, and one that is highly relevant to methods that are … Read more
The standard quadratic program (QPS) is $\min_{x\in\Delta} x’Qx$, where $\Delta\subset\Re^n$ is the simplex $\Delta=\{ x\ge 0 : \sum_{i=1}^n x_i=1 \}$. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One … Read more
We consider the problem of global minimization of rational functions on $\LR^n$ (unconstrained case), and on an open, connected, semi-algebraic subset of $\LR^n$, or the (partial) closure of such a set (constrained case). We show that in the univariate case ($n=1$), these problems have exact reformulations as semidefinite programming (SDP) problems, by using reformulations introduced … Read more
SIAM’s SIAG/Opt Newsletter special issue on Large Scale Nonconvex Optimization. Guest editors Sven Leyffer and Jorge Nocedal, with contributions by Gould, Sachs, Biegler, Waechter, Leyffer, Bussieck and Pruessner. CitationSIAG/Opt Views-and-News, Volume 14 Number 1, April 2003. http://fewcal.uvt.nl/sturm/siagopt/ArticleDownload View PDF
In this paper we study the relationship between bilevel optimization and bicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower level problem of the bilevel optimization problem … Read more
We obtain rigorous estimates for linear and semidefinite relaxations of global optimization problems on the simplex and on the sphere CitationResearch report, February, 2003ArticleDownload View PDF
In this paper we report results on the problem of docking two large proteins by means of a two-phase monotonic basin hopping method. Given an appropriate force field which is used to measure the interaction energy between two biomolecules which are considered as rigid bodies, we used a randomized global optimization methods based upon the … Read more
We recently discovered 5 new putative globally optimum configurations for Morse clusters at $\rho=8$. This report contains some algorithmic details as well as the structures determined with our method. CitationTechnical Report DSI 3-2003, Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Firenze, 2003.ArticleDownload View PDF