Journal of Applied and Numerical Optimization

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DOI: 10.23952/jano.3.2021.2.10
Volume 3, Issue 2, 31 August 2021, Pages 425-434

 

Abstract. E.G. Belousov and V.G. Andronov [Solvability and Stability of Problems of Polynomial Programming (in Russian), Publishing House of the Moscow University, Moscow, p.4, 1993] have observed that the notions of structural convexity and ravine of a polynomial function, which were introduced by themselves, are useful for studying stability and solvability of convex polynomial mathematical programming problems, as well as for the investigation of the distribution of integer points in convex sets. The results given in Chapters 3-5 of the book justify their observations. This paper presents some facts about structural convexity and ravines of quadratic functions. Among other things, we obtain a verifiable criterion for structural convexity of a quadratic function and show that such a function cannot have ravines along linear subspaces.

 

How to Cite this Article:
N.N. Tam, C.-F. Wen, J.-C. Yao, N.D. Yen, Structural convexity and ravines of quadratic functions, J. Appl. Numer. Optim. 3 (2021), 425-434.