Generalized entropy optimization problems and the existence of their solutions

Shamilov A.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, vol.382, no.2, pp.465-472, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 382 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1016/j.physa.2007.04.014
  • Journal Name: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.465-472
  • Keywords: entropy optimization problem, Newton's method, existence theorem, a priori evaluation
  • Anadolu University Affiliated: No

Abstract

In the present study we have formulated a generalization of entropy optimization problems (GEOP), proposed sufficient conditions for the existence of solution. We have suggested also a new method based on a priori evaluations and Newton's methods for calculation of Langrange multipliers. Mentioned method allows calculating Langrange multipliers by starting from arbitrary initial point for Newton's approximations of constructed auxiliary equation. The solution of auxiliary equation is chosen as initial point for second constructed auxiliary equation. The recurring mentioned process for finite time leads to achieve an initial point for Newton's approximations of given equation and allows to find its unknown solution. (C) 2007 Elsevier B.V. All rights reserved.