We shall extend Iri's multiplicative penalty function method for linear programming [41 so that it can handle the problem of unknown optimum value of the objective function, without solving both primal and dual problems simultaneously, and generate convergent dual solutions. By making use of these dual variables, lower bounds of the optimum objective function value are updated efficiently, whic...

This paper presents a new multiplicative algorithm for nonnegative matrix factorization with β-divergence. The derived update rules have a similar form to those of the conventional multiplicative algorithm, only differing through the presence of an exponent term depending on β. The convergence is theoretically proven for any real-valued β based on the auxiliary function method. The convergence ...

It is known that if f is a multiplicative increasing function on N, then either f(n) = 0 for all n∈N or f(n) = n for some ¿0. It is very natural to ask if there are similar results in other algebraic systems. In this paper, we 1rst study the multiplicative increasing functions over nonnegative square matrices with respect to tensor product and then restrict our result to multidigraphs and loopl...

We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior in the formation of large scale spatial correlations as a function of the multiplicative colored noise intensity. This behavior is shifted towards higher val...

New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.

This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant. Theorem 6.2 describes a class of non-polyconvex but multiplicative quasiconvex isotropic functions. Relevance of...

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.