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A globally convergent primal-dual interior-point 3D filter method for nonlinear SDP

Zhongyi Liu (zhyi***at***hhu.edu.cn)

Abstract: This paper proposes a primal-dual interior-point filter method for nonlinear semidefinite programming, which is the first multidimensional (three-dimensional) filter methods for interior-point methods, and of course for constrained optimization. A freshly new definition of filter entries is proposed, which is greatly different from those in all the current filter methods. A mixed norm is used to tackle with trust region constraints and global convergence to first-order critical points can easily be proved by slightly modifying the analysis in Ulbrich et al.\cite{Ulbrich-04}.

Keywords: nonlinear SDP, interior-point methods, 3D filter, global convergence

Category 1: Nonlinear Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

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Entry Submitted: 10/19/2008
Entry Accepted: 10/19/2008
Entry Last Modified: 08/11/2009

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