Tilt Stability for Quadratic Programs with One or Two Quadratic Inequality Constraints


This paper examines tilt stability for quadratic programs with one or two quadratic inequality constraints. Exploiting specific features of these problems and using some known results on tilt stability in nonlinear programming, we establish quite simple characterizations of tilt-stable local minimizers for quadratic programs with one quadratic inequality constraint under metric subregularity constraint qualification. By the same way, we also derive various tilt stability conditions for quadratic programs with two quadratic inequality constraints and satisfying certain suitable assumptions. Especially, the obtained results show that some tilt stability conditions only known to be sufficient in nonlinear programming become the necessary ones when the considered problems are quadratic programs with one or two quadratic inequality constraints.

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The authors would like to thank the referee and the Handling Editor for their valuable comments and kind suggestions.


This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2017.325.

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Correspondence to Nguyen Huy Chieu.

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Dedicated to Professor Hoang Tuy on the occasion of his 90th birthday

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Chieu, N.H., Van Hien, L. & Trang, N.T.Q. Tilt Stability for Quadratic Programs with One or Two Quadratic Inequality Constraints. Acta Math Vietnam 45, 477–499 (2020). https://doi.org/10.1007/s40306-020-00372-4

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  • Tilt stability
  • Strong second-order sufficient condition
  • Metric subregularity constraint qualification
  • Quadratic program
  • Quadratic inequality constraint

Mathematics Subject Classification (2010)

  • 49J53
  • 90C31
  • 90C46