On geometry and convergence of a class of simplicial covers

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

Keywords:

• Concave Minimization
• Global Optimization
• Simplicial Covers
• Convergence Conditions