Acta Mathematica Vietnamica

, Volume 43, Issue 1, pp 155–174 | Cite as

On the Solution Existence of Nonconvex Quadratic Programming Problems in Hilbert Spaces

  • Vu Van DongEmail author
  • Nguyen Nang Tam


We propose conditions for the existence of solutions for nonconvex quadratic programming problems whose constraint set is defined by finitely many convex linear-quadratic inequalities in Hilbert spaces. In order to obtain our results, we use either properties of the Legendre form or properties of compact operators with closed range. The results are established without requesting the convexity of the objective function or the compactness of the constraint set. As a special case, we obtain some on the existence of solutions results for the quadratic programming problems under linear constraints in Hilbert spaces.


Quadratic program in Hilbert spaces Convex quadratic constraints Solution existence Legendre form Recession cone Compact operator with closed range 

Mathematics Subject Classification (2010)

90C20 90C26 90C30 



This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.39. The authors would like to thank Prof. N. D. Yen for valuable remarks and suggestions. The authors would like to express our sincere thanks to the anonymous referees and editors for insightful comments and useful suggestions.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Phuc Yen College of IndustryPhucyenVietnam
  2. 2.Hanoi Pedagogical Institute 2HanoiVietnam

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