First and second order analysis of nonlinear semidefinite programs
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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.
KeywordsSemidefinite programming Cone constraints Convex programming Duality Second-order optimality conditions Tangent cones Optimal value function Sensitivity analysis
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- F. Alizadeh, Combinatorial optimization with interior point methods and semi-definite matrices, Ph.D. Thesis, University of Minnesota, 1991.Google Scholar
- F. Alizadeh, J.-P.A. Haeberly and M.L. Overton, Primal-dual interior-point methods for semidefinite programming, preprint, presented at theXV Symposium on Mathematical Programming, Ann Arbor, 1994.Google Scholar
- J.F. Bonnans, R. Cominetti and A. Shapiro, Second order necessary and sufficient optimality conditions under abstract constraints, Preprint.Google Scholar
- E.G. Gol’shtein,Theory of Convex Programming, Translations of Mathematical Monographs, Vol. 36 (American Mathematical Society, Providence, RI, 1972).Google Scholar
- G. Pataki, On the multiplicity of optimal eigenvalues, Management Science Research Report #MSRR-604, GSIA, Carnegie Mellon University.Google Scholar
- A. Shapiro, On uniqueness of Lagrange multipliers in optimization problems subject to cone constraints,SIAM J. on Optimization, to appear.Google Scholar