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Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming

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In this paper it is shown that, in the absence of any regularity condition, sequential Lagrangian optimality conditions as well as a sequential duality results hold for abstract convex programs. The significance of the results is that they yield the standard optimality and duality results for convex programs under a simple closed-cone condition that is much weaker than the well-known constraint qualifications. As an application, a sequential Lagrangian duality, saddle-point conditions, and stability results are derived for convex semidefinite programs.

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The authors are grateful to the referee and Professor Franco Giannessi for valuable comments and constructive suggestions which have contributed to the final preparation of the paper.

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Dinh, N., Jeyakumar, V. & Lee, G.M. Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming. J Optim Theory Appl 125, 85–112 (2005).

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