On Some Special Matrix Classes Useful in Optimization and Game Theory

The well-known problem of checking copositivity is equivalent to solving a quadratic optimization problem over the standard simplex. This is an object of research for a long time. This paper presents some results related to the well-known matrix classes like copositive, semimonotone matrices discussed in the literature for many years. We relate some important theorems of alternatives with the class of copositive-plus and copositive-star matrices. Finally, we revisit the classes of almost copositive, semimonotone matrices and obtain some new results which are useful in optimization theory. Finally, we present some game theoretic characterizations of these special class of matrices.