{
"title": "Probability of Globality",
"authors": "Eva Eggeling, Dieter W. Fellner, Torsten Ullrich",
"country": null,
"institution": null,
"volume": "73",
"journal": "International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering",
"pagesStart": 36,
"pagesEnd": 41,
"ISSN": "1307-6892",
"URL": "http:\/\/waset.org\/publications\/6040",
"abstract": "The objective of global optimization is to find the\nglobally best solution of a model. Nonlinear models are ubiquitous\nin many applications and their solution often requires a global\nsearch approach; i.e. for a function f from a set A \u2282 Rn to\nthe real numbers, an element x0 \u2208 A is sought-after, such that\n\u2200 x \u2208 A : f(x0) \u2264 f(x). Depending on the field of application,\nthe question whether a found solution x0 is not only a local minimum\nbut a global one is very important.\nThis article presents a probabilistic approach to determine the\nprobability of a solution being a global minimum. The approach is\nindependent of the used global search method and only requires a\nlimited, convex parameter domain A as well as a Lipschitz continuous\nfunction f whose Lipschitz constant is not needed to be known.",
"references": null,
"publisher": "World Academy of Science, Engineering and Technology",
"index": "International Science Index 73, 2013"
}