A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff games. Moreover, any combinatorial simplex algorithm with a strongly polynomial complexity (the existence of such an algorithm is open) would provide in this way ...

Abstract A real symmetric matrix is copositive if $$x^\top Ax\ge 0$$ x ⊤ A ≥ 0 for all $$x\ge . As and only it on the standard simplex, algorithms to determine copositivity, such as those in Spons...

Abstrac/-This paper proposes a new parallel search algorithm using evolutionary programming and quasi-simplex technique (EPQS). EPQS produces the offspring from three ways in parallel: 1) Using the Gaussian mutation, 2) Using the Cauchy mutation, and 3) Using the quasi-simplex techniques. The quasi-simplex technique uses the ideal of classical simplex technique and produces four prospective ind...

This paper presents a new inhomogeneous solid modeling paradigm for engineering design. The proposed paradigm can represent, model, and render multi-dimensional, physical attributes across any volumetric objects of complicated geometry and topology. A modeled object is formulated with a trivariate simplex spline defined over a tetrahedral decomposition of its 3D domain. Heterogeneous material a...