A new exclusion test

Exclusion tests are a well-known tool for obtaining all solutions of a nonlinear system of equations, see, e.g., the work of Krawczyk or Moore. Recently, Yamamura and collaborators have developed Linear Programming exclusion tests that turned out to be highly successful for nonlinear problems in electrical networking. The author has developed higher order exclusion tests based on Taylor expansions. In the present paper it is shown that the ideas behind both approaches can be combined: We present a new class of higher order Linear Programming exclusion tests, investigate their computational complexity, and illustrate their performance on several examples.