Using P0-simple functionals, we generalise the result from Theorem 1.1 obtained by Professor F. Qi (F. QI, An algebraic inequality, RGMIA Res. Rep. Coll., 2(1) (1999), article 8).

We examine a multidimensional optimisation problem in the tropical mathematics setting. The problem involves the minimisation of a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear inequality constraints. We start with an overview of known tropical optimisation problems with linear and nonlinear objective functions. A short introduction...

Abstract In this paper the existing simplex splitting algorithm for finding a feasible solution of systems of linear inequalities is modified by evolving a vertex-determination technique. The existing algorithm cannot determine when the system of linear inequalities is infeasible hence the need for a modification. The modified algorithm is able to determine the feasible solution whenever it exi...

Even taking into account the sobering lessons learned from the recession, affordable homeownership remains the most important wealth-building opportunity for most LMI families.1 A major long-term macroeconomic benefit will be achieved if our mortgage finance system effectively opens access to those populations that will make up the largest portion of the growth of the mortgage market in the com...

Let k3(n) denote the minimal cardinality of a ternary code of length n and covering radius one. In this paper we show k3(7) ≥ 156 and k3(8) ≥ 402 improving on the best previously known bounds k3(7) ≥ 153 and k3(8) ≥ 398. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in k...

Schoute (1911) introduced the permutahedron on an n-element set N= { 1, . . . , n} as follows. With any permutation n of N we associate an incidence vector x(71) = (n(I), *.., n(n)) E IR”. The permutahedron is the polytope Perm(N) = conv{x(rr): rr is a permutation of N}. Independently, several authors (cf., e.g., Rado [4], Balas [l], Gaiha and Gupta [2], Young [6]) studied the permutahedron and...

This paper is concerned with a KYP-type result for descriptor systems. Matrix inequalities are shown that provide necessary and sufficient conditions of dissipativity of descriptor systems, without such restriction on the realization of descriptor systems as in many of previous results. Furthermore, LMI conditions are presented for synthesis of control gains to attain dissipativity of feedback ...