Abstract
This article presents the fundamental mathematical properties of new simplicial and conical solution methods for concave minimization problems which uses a new simplicial cover rather than the classical radial partitioning techniques. In particular, a number of conditions is derived which ensure convergence of every decreasing sequence of simplices generated by the new technique to a singleton, a property which is fundamental for the convergence of related optimization methods. Moreover, a new estimate of the outer radius-diameter ratio is derived for generalized bisection
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