Global optimization

Abstract

The optimization community has long been interested in solving multiextremal optimization problems to global optimality. Some of the first exact approaches to nonconvex nonlinear programs (NLPs) and mixed-integer nonlinear programs (MINLPs) relied on convexification via cutting planes [23], as well as branch-and-bound, i.e. bounding combined with progressive partitioning of the space of continuous, in addition to integer, variables [9]. Approximations based on the a priori discretization of nonlinear functions were also proposed and capitalized on the availability of fast linear integer programming techniques [3]. Activities in the field of global optimization started to intensify in the early 1990s, when the Journal of Global Optimization was launched. Today, the global optimization community has grown considerably, as evidenced by flourishing publications and conference activities in this area. The book by Horst and Tuy [11], an indispensable resource for anyone working in this area, has received over 1200 citations (according to Google Scholar as of 17 June 2009). At the same time, the 20th International Symposium on Mathematical Programming (Chicago, 2009) is scheduled to include 20 sessions in its global optimization cluster, with many additional related sessions in its MINLP cluster. Clearly, global optimization has grown into an area of major focus in the field of mathematical programming over the past two decades.The purpose of this special issue is to showcase current research activities in the area of global optimization. The papers of this issue reflect the broad range of activities in this area and address deterministic as well as stochastic algorithms, the development of software and computational experience with a variety of algorithms, and a number of applications in engineering and science. Corresponding to these three thematic areas, the papers have been grouped into three parts. Part 1 -Theory and algorithmsIn the first part, there are five papers that present and analyse, mostly theoretically, a variety of algorithms and methodologies:• Contrary to the widespread practice of building relaxations of nonconvex problems by outer approximating one term of a nonconvex constraint at a time, Bao et al. [2] investigate relaxations that consider multiple terms simultaneously.

The Investigation on the Engineering University Students’ Entrepreneurial Quality

“…Currently, there are lots of benchmark test datasets for global optimization such as the wellknown GLOBALLib [18], MINLPLib [20] and DIRECTGOLib [25]. Unfortunately, none of them are specifically for checking and testing the performance of GOA on nonlinear curve fitting.…”

“…The fitting function and corresponded data for all 38 test problems are shown in Table 2, where x and y represent the independent and dependent variables, respectively, and b is the parameter vector. [5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95]; y= [3.3,6.5,9.2,11.9,14.5,17.0,19.4,21.7,23.9,25.9…”