Optimality Conditions in Semidefinite Programming

Abstract

Semidefinite positiveness of operators on Euclidean spaces is characterized. Using this characterization, we compute in a direct way the first-order and second-order tangent sets to the cone of semidefinite positive operators on such a space. These characterizations are useful for optimality conditions in semidefinite programming.

Keywords:

• Cone programming
• Manifold with corners
• Optimality condition
• Semidefinite programming
• Tangent cone
• Tangent set of order two

Mathematics Subject Classification:

• 90C22
• 90C26
• 90C46

Acknowledgments

Part of the special issue, “Variational Analysis and Applications.”