On one method of analysis of a polynomial on constancy of signs in the positive orthant

Аuthors

Nefedov V. N.

Abstract

The present article is the continuation of the articles [1-3], in which the problem of constructing the applicable in practice necessary and sufficient conditions of the positivity (or nonnegativity) of a polynomial in several variables with real coefficients in the positive orthant was investigated. In the articles [1,2] the necessary condition and some sufficient conditions were received. In the article [3] the necessary and sufficient condition was received without any restrictions on the polynomial. But the applicable in practice method of verification of fulfilment of this condition was described in [3] for the special class of the polynomials. One of the basic ideas of this method consists in use of the methods of vector optimization. In the present article the same (as in [3]) necessary and sufficient condition is used and the method of verification of fulfilment of this condition also makes use of the methods of vector optimization. But the verification method prescribed in this article does not require any conditions on the investigated polynomial.

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