Abstract
In this paper, we present a QP-free algorithm for nonlinear semidefinite programming. At each iteration, the search direction is yielded by solving two systems of linear equations with the same coefficient matrix; l_{1} penalty function is used as merit function for line search, the step size is determined by Armijo type inexact line search. The global convergence of the proposed algorithm is shown under suitable conditions. Preliminary numerical results are reported.
Highlights
Consider the following nonlinear semidefinite programming (NLSDP for short): min f (x) s.t
NLSDPs have been attracting a great deal of research attention [, – ]
In this paper, motivated from QP-free method for standard nonlinear programs, based on techniques of perturbation and penalty function, we propose a globally convergent QP-free algorithm for NLSDP ( . )
Summary
Consider the following nonlinear semidefinite programming (NLSDP for short): min f (x) s.t. For the sake of convenience, some results on matrix analysis and NLSDP are restated which will be employed in the following analysis of the proposed algorithm. The following lemma gives a sufficient condition of the assumption A .
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