Optimality conditions and global convergence for nonlinear semidefinite programming

  • Roberto Andreani
  • Gabriel HaeserEmail author
  • Daiana S. Viana
Full Length Paper Series A


Sequential optimality conditions have played a major role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization. In this paper, we extend theses concepts for nonlinear semidefinite programming. We define two sequential optimality conditions for nonlinear semidefinite programming. The first is a natural extension of the so-called Approximate-Karush–Kuhn–Tucker (AKKT), well known in nonlinear optimization. The second one, called Trace-AKKT, is more natural in the context of semidefinite programming as the computation of eigenvalues is avoided. We propose an augmented Lagrangian algorithm that generates these types of sequences and new constraint qualifications are proposed, weaker than previously considered ones, which are sufficient for the global convergence of the algorithm to a stationary point.


Nonlinear semidefinite programming Optimality conditions Constraint qualifications Practical algorithms 

Mathematics Subject Classification

90C22 90C46 90C30 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of CampinasCampinasBrazil
  2. 2.Department of Applied MathematicsUniversity of São PauloSão PauloBrazil
  3. 3.Center of Exact and Technological SciencesFederal University of AcreRio BrancoBrazil

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