On determining the cover of a simplex by spheres centered at its vertices
Journal of Global Optimization
Global optimization simplex bisection revisited based on considerations by reiner horst
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
A threaded approach of the quadratic bi-blending algorithm
The Journal of Supercomputing
Simplicial Lipschitz optimization without the Lipschitz constant
Journal of Global Optimization
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The blending problem is studied as a problem of finding cheap robust feasible solutions on the unit simplex fulfilling linear and quadratic inequalities. Properties of a regular grid over the unit simplex are discussed. Several tests based on spherical regions are described and evaluated to check the feasibility of subsets and robustness of products. These tests have been implemented into a Branch-and-Bound algorithm that reduces the set of points evaluated on the regular grid. The whole is illustrated numerically.