The Faculty of Information Technology and Development Centre and the Veszprém Regional Committee of the Hungarian Academy of Sciences (MTA-VEAB) jointly organized the second Veszprém Optimization Conference: Advanced Algorithms (VOCAL) on December 13–15, 2006.
The conference focused on recent advances in optimization algorithms – continuous and discrete. Complexity and convergence properties, high performance optimization software, and novel applications were also reviewed. The aim of the organizers was to bring together researchers from both the theoretical and applied optimization communities in the framework of a medium-scale event. During the three days of the conference, internationally renowned researchers from 20 countries of four continents delivered more than 70 presentations to give an overview of their latest achievements. The central theme of the conference, similar to 2004, was mathematical and computational theory, and practical problems of optimization methods, including modelling, analysis, and optimization of complex industrial systems.
The purpose of this event was to bring together leading-edge researchers, to provide an opportunity to reflect the state of the art of the optimization area, to discuss challenges and trends.
We take this opportunity to express our warm-hearted thanks to the International Scientific Committee. The members of the Scientific Committee were: Andrew R. Conn, Komei Fukuda, Florian Jarre, Jakob Krarup, Arnold Neumaier, Gianni Di Pillo, Franz Rendl, Kees Roos, and Jean-Philippe Vial. We also thank the Organizing Committee: Tibor Csendes, Aurél Galántai, Tibor Illés, Sándor Komlósi, István Maros, Zsolt Páles, Tamás Szántai, and László Szeidl. This special issue presents some of the highlights of the conference.
Gundersen and Steihaug's paper ‘On large-scale unconstrained optimization problems and higher order methods’ demonstrates that, for a large class of problems, the ratio of the number of arithmetic operations of Halley's method and Newton's method is constant per iteration. It is shown that (One Step Halley)/(One Step Newton) ≤ 5. The paper shows that the zero elements in the Hessian matrix induce zero elements in the third derivative as well.
Gratton et al. consider an implementation of the recursive multilevel trust-region algorithm for bound-constrained nonlinear problems, and present numerical experiences on multilevel test problems. The algorithm's parameters are identified on these problems, yielding a satisfactory compromise between reliability and efficiency.
El Ghami et al. present a class of polynomial-time primal–dual interior-point methods for semidefinite optimization based on a new class of kernel functions.
Ivanov and de Klerk introduce an algorithmic framework and practical aspects of implementing a parallel version of a primal–dual semidefinite programming solver on a distributed memory computer cluster. The significant improvement is obtained for a test set of problems with rank one constraint matrices.
Angelelli et al. consider the problem of semi on-line scheduling on two uniform processors, in the case where the total sum of the tasks is known in advance. The developed geometric representation can be applied to improve on the currently known best bounds on the competitive ratio of semi on-line scheduling algorithms.
Nasrabadi and Hashemi study a minimum cost flow problem in networks where the transit cost/time/capacity of each arc, as well as the demand/supply and storage cost/capacity of each node, can change over discrete time steps.
Mészáros investigates how computers with CPUs of multiple computing cores perform in computational practice of interior point methods. The paper focuses on the implementation of Cholesky factorization of large-scale and sparse symmetric positive semidefinite matrices.
Koluaei and Terlaky present an extension of a recent variant of Mehrotra's predictor–corrector algorithm to semidefinite optimization, which has been proposed by Salahi et al. in 2005 for linear optimization problems. Based on the Nesterov–Todd direction as Newton search direction they show that the iteration-complexity bound of the algorithm is of the same order as that of the corresponding algorithm for the case of linear optimization.