Abstract

We prove in this paper the stability of the Lagrangian duality in nonconvex quadratic minimization over Euclidean balls and spheres. As direct consequences we state both global optimality conditions in these problems and detailed descriptions of the structure of their solution sets. These results are essential for devising solution algorithms.

Author information

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Pham Dinh Tao

Mathematical Modelling and Applied Optimization Group, LMI, INSA Rouen, CNRS, URA 1378. BP 8, 76131 Mont Saint Aignan Cedex, France.

Le Thi Hoai An

Mathematical Modelling and Applied Optimization Group, LMI, INSA Rouen, CNRS, URA 1378. BP 8, 76131 Mont Saint Aignan Cedex, France.

Keywords

  • nonconvex quadratic minimization
  • stability of Lagrangian duality
  • global optimality conditions

References

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Suggested citation

Pham Dinh Tao, Le Thi Hoai An. “Lagrangian Stability and Global Optimality in Nonconvex Quadratic Minimization over Euclidean Balls and Spheres.” Journal of Convex Analysis 2 (1995), No. 1&2, 263–276. https://doi.org/10.68381/jca02017

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Published by Heldermann Verlag, 1995. Rights now held by Banach Press LLC.