Some Stability Properties of Parametric Quadratically Constrained Nonconvex Quadratic Programs in Hilbert Spaces
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Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal value function, assuming that the problem data undergo small perturbations.
KeywordsQuadratic program in Hilbert spaces Convex quadratic constraints Solution existence Legendre form Recession cone Solution set Solution map Optimal value function
Mathematics Subject Classification (2010)90C20 90C30 90C31
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.39. The author would like to thank Prof. Nguyen Nang Tam for valuable remarks and suggestions. The author would like to express his sincere thanks to the anonymous referees and editors for insightful comments and useful suggestions.
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