Mathematical Programming

, Volume 77, Issue 1, pp 301–320 | Cite as

First and second order analysis of nonlinear semidefinite programs

  • Alexander Shapiro


In this paper we study nonlinear semidefinite programming problems. Convexity, duality and first-order optimality conditions for such problems are presented. A second-order analysis is also given. Second-order necessary and sufficient optimality conditions are derived. Finally, sensitivity analysis of such programs is discussed.


Semidefinite programming Cone constraints Convex programming Duality Second-order optimality conditions Tangent cones Optimal value function Sensitivity analysis 


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Copyright information

© The Mathematical Programming Society, Inc 1997

Authors and Affiliations

  • Alexander Shapiro
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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