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| Volume 4, Number 1, January 2008, pp. 153-176 | |||||||||
| Gleb Beliakov | |||||||||
| Key words: | |||||||||
| global optimization, Lipschitz optimization, abstract convexity, cutting angle method, saw-tooth underestimate | |||||||||
| Mathematices Subject Classification: 90C26, 65K05, 90C56, 65K10 | |||||||||
|
|||||||||
| Volume 4, Number 1, January 2008, pp. 153-176 | |||||||||
| Gleb Beliakov | |||||||||
| Key words: | |||||||||
| global optimization, Lipschitz optimization, abstract convexity, cutting angle method, saw-tooth underestimate | |||||||||
| Mathematices Subject Classification: 90C26, 65K05, 90C56, 65K10 | |||||||||
|
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| Abstract: | |||
| Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach. | |||
| Extended cutting angle method of global optimization | ||