A Subspace Version of the Powell–Yuan Trust-Region Algorithm for Equality Constrained Optimization


Abstract This paper studied subspace properties of the Celis–Dennis–Tapia (CDT) subproblem that arises in some trust-region algorithms for equality constrained opti-mization. The analysis is an extension of that presented by Wang and Yuan (Numer. Math. 104:241–269, 2006) for the standard trust-region subproblem. Under suitable conditions, it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current iteration. Based on this observation, a sub-space version of the Powell–Yuan trust-region algorithm is proposed for equality con-strained optimization problems where the number of constraints is much lower tha

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