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Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming

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Abstract

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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Authors and Affiliations

  1. Associate Professor, Department of Mathematics and Computer Science, University of Pedagogy, Ho Chi Minh City, Vietnam

    N. Dinh

  2. Pukyong National University, Pusan, Korea

    N. Dinh

  3. Head, Department of Applied Mathematics, University of New South Wales, Sydney, NSW, Australia

    V. Jeyakumar

  4. Professor, Department of Applied Mathematics, Pukyong National University, Pusan, Korea

    G. M. Lee

Authors
  1. N. Dinh
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  2. V. Jeyakumar
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  3. G. M. Lee
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Additional information

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). https://doi.org/10.1007/s10957-004-1712-8

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  • DOI: https://doi.org/10.1007/s10957-004-1712-8

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