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Semidefinite programming via image space analysis

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  • In this paper, we investigate semidefinite programming by using the image space analysis and present some equivalence between the (regular) linear separation and the saddle points of the Lagrangian functions related to semidefinite programming. Some necessary and sufficient optimality conditions for semidefinite programming are also given under some suitable assumptions. As an application, we obtain some equivalent characterizations for necessary and sufficient optimality conditions for linear semidefinite programming under Slater assumption.
    Mathematics Subject Classification: Primary: 90C22, 65K10.


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