An algorithm for finding the global maximum of a multimodal, multivariate function
Mathematical Programming: Series A and B
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
A rejection technique for sampling from T-concave distributions
ACM Transactions on Mathematical Software (TOMS)
Estimation of the Lipschitz Norm with Neural Networks
Neural Processing Letters
A sweep-plane algorithm for generating random tuples in simple polytopes
Mathematics of Computation
Fast Algorithm for the Cutting Angle Method of Global Optimization
Journal of Global Optimization
Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications)
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The acceptance/rejection approach is widely used in universal nonuniform random number generators. Its key part is an accurate approximation of a given probability density from above by a hat function. This article uses a piecewise constant hat function, whose values are overestimates of the density on the elements of the partition of the domain. It uses a sawtooth overestimate of Lipschitz continuous densities, and then examines all local maximizers of such an overestimate. The method is applicable to multivariate multimodal distributions. It exhibits relatively short preprocessing time and fast generation of random variates from a very large class of distributions.