Infeasibility spheres for finding robust solutions of blending problems with quadratic constraints

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.