Abstract
Recently a method based on substitution of difference of variables has been developed by Yang [12] for verifying the positive semi-definiteness of homogeneous polynomials. In this paper, we investigate the structure of the cone formed by all symmetric homogeneous polynomials whose positive semi-definiteness can proven by difference substitution method.
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References
Bertsekas, D.P., Nedić, A., Ozdaglar, A.E.: Convex analysis and optimization, pp. 25–45. Athena Scientific and Tsinghua University Press (2006)
Chen, S.L., Yao, Y.: Schur Subspace of Real Symmetric Forms and Application. Acta Mathematica Sinica, Chinese Series 50, 1331–1348 (2007)
Chernikova, N.V.: Algorithm for finding a general formula for the non-negative solutions of a system of linear equations. U.S.S.R Computational Mathematics and Mathematical Physics 4, 151–158 (1964)
Chernikova, N.V.: Algorithm for finding a general formula for the non-negative solutions of a system of linear inequalities. U.S.S.R Computational Mathematics and Mathematical Physics 5, 228–233 (1965)
Chernikova, N.V.: Algorithm for discovering the set of all the solutions of a linear programming problem. U.S.S.R Computational Mathematics and Mathematical Physics 8, 282–293 (1968)
Fernández, F., Quinton, P.: Extension of Chernikova’s algorithm for solving general mixed linear programming problems, Technical Report 437, IRISA-Rennes, France (1988)
Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities, 2nd edn., pp. 57–59. Cambridge University Press, Cambridge (1952)
Huang, F.J., Chen, S.L.: Schur partition for symmetric ternary forms and readable proof to inequalities. In: ISSAC 2005, Beijing, China, pp. 185–192 (2005)
Rabl, T.: Volume calculation and estimation of parameterized integer polytopes, Diploma Thesis, Universität Passau, German (2006)
Wilde, D.K.: A library for doing polyhedral operations, Technical Report 785, IRISA-Rennes, France (1993)
Verge, H.L.: A note on Chernikova’s algorithm, Technical Report 635, IRISA-Rennes, France (1994)
Yang, L.: Solving harder problems with lesser mathematics. In: Ju, C., Korea, S., Chu, S.-C., et al. (eds.) ATCM 2005, pp. 37–46. ATCM Inc., Blacksburg (2005)
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Chen, L., Zeng, Z. (2008). Which Symmetric Homogeneous Polynomials Can Be Proved Positive Semi-definite by Difference Substitution Method?. In: Kapur, D. (eds) Computer Mathematics. ASCM 2007. Lecture Notes in Computer Science(), vol 5081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87827-8_5
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DOI: https://doi.org/10.1007/978-3-540-87827-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87826-1
Online ISBN: 978-3-540-87827-8
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