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International Journal of Mathematical Research

August 2014, Volume 3, 4, pp 37-48

Applied Optimization and Approximation

Octav Olteanu

Octav Olteanu 1

  1. Department of Mathematics - Informatics, University Politehnica of Bucharest, Bucharest, Romania 1

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Abstract:

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.
Contribution/ Originality
The paper contributes the first logical analysis of the problems solved in the theorems 2.1, 2.2 (optimization in kinematics), 3.3 (minimization of the total cost), Lemma 4.2 (approximation), Theorem 4.3 (solving the moment problem). The paper’s primary contribution is finding that suitable polynomial approximation yields solving the multidimensional moment problem. This study documents how practical and theoretical  problems can be solved.

Keywords:


Reference:

  1. O. Olteanu, "Kinematics and optimization in railway transport", National Railway Stock Symposium, X - th Edition, Presented Works, November, 23-24 2012, Matrix Rom, Bucharest, (In Romanian), 2012.
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  11. A. Olteanu and O. Olteanu, "Some unexpected problems of the moment problem," in Proc. of the Sixth Congress of Romanian Mathematicians, Ed. Academiei, Vol. I (Scientific Contributions), Bucharest, 2009, pp. 347-355.
  12. O. Olteanu, "Application de théorèmes de prolongement d’opérateurs linéaires au problème des moments et à une généralisation d’un théorème de Mazur-Orlicz," C. R. Acad. Sci. Paris 313, Série I, pp. 739-742, 1991.
  13. O. Olteanu, Geometric aspects in operator theory and applications. Saarbr?cken: Lambert Academic Publishing, 2012.
  14. O. Olteanu, "Moment problems on bounded and unbounded domains," International Journal of Analysis, Article ID 524264. Available: http://dx.doi.org/10.1155/2013/524264, vol. 2013, p. 7, 2013.
  15. O. Olteanu, "New results on Markov moment problem," International Journal of Analysis, Article ID 901318. Available: http://dx.doi.org/10.1155/2013/901318, vol. 2013, p. 17, 2013.
  16. O. Olteanu, "Approximation and Markov moment problem on concrete spaces," Rendiconti del Circolo Matematico di Palermo, vol. 63, pp. 161-172, 2014.
  17. M. Putinar and F. H. Vasilescu, "Problème des moments sur les compacts semi-algébriques," C. R. Acad. Sci. Paris, 323, Série I, pp. 787-791, 1996.

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