Journal ArticleDOI
An algorithm for finding the global maximum of a multimodal, multivariate function
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This algorithm for global optimization uses an arbitrary starting point, requires no derivatives, uses comparatively few function evaluations and is not side-tracked by nearby relative optima, so as to build a gradually closer piecewise-differentiable approximation to the objective function.Abstract:
This algorithm for global optimization uses an arbitrary starting point, requires no derivatives, uses comparatively few function evaluations and is not side-tracked by nearby relative optima. The algorithm builds a gradually closer piecewise-differentiable approximation to the objective function. The computer program exhibits a (theoretically expected) strong tendency to cluster around relative optima close to the global. Results of testing with several standard functions are given.read more
Citations
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Journal ArticleDOI
Towards Pure Adaptive Search - A general framework and a one-dimensional realisation
TL;DR: In this article, the authors introduce a new algorithm termed Pure Localisation Search (PLS) which attempts to reach the practical ideal for a certain class of one variable functions, where the gap is bridged.
Journal ArticleDOI
Improved Lipschitz bounds with the first norm for function values over multidimensional simplex
R. Paulavièius,Julius Žilinskas +1 more
TL;DR: In this article, a branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function.
Journal ArticleDOI
Global optimization using the branch‐and‐bound algorithm with a combination of Lipschitz bounds over simplices
TL;DR: The efficiency of the proposed global optimization algorithm is evaluated experimentally and compared with the results of other well‐known algorithms, and the proposed algorithm often outperforms the comparable branch‐and‐bound algorithms.
Journal ArticleDOI
Global Continuous Optimization with Error Bound and Fast Convergence
TL;DR: A new global optimization algorithm, called Locally Oriented Global Optimization (LOGO), to aim for both fast convergence in practice and finite-time error bound in theory, and is applied to accident management of a nuclear power plant.
Book ChapterDOI
Exact Penalty Function Methods for Nonlinear Semi-Infinite Programming
TL;DR: The extension of standard theory to the semi-infinite case is illustrated through simple examples and some of the theoretical and computational difficulties are highlighted.
References
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Journal ArticleDOI
Sequential minimax search for a maximum
TL;DR: The problem formulated below was motivated by that of determining an interval containing the point at which a unimodal function on the unit interval possesses a maximum, without postulating regularity conditions involving continuity, derivatives, etc.
Journal ArticleDOI
A Sequential Method Seeking the Global Maximum of a Function
TL;DR: In this article, a sequential search method for finding the global maximum of an objective function is proposed, which is applicable to a single variable defined on a closed interval and such that some bound on its rate of change is available.
Journal ArticleDOI
An algorithm for finding the absolute extremum of a function
TL;DR: A general algorithm for finding the absolute minimum of a function to a given accuracy is described and special aspects of its application are illustrated by examples involving functions of one or more variables, satisfying a Lipschitz condition.