Abstract
This paper studied subspace properties of the Celis–Dennis–Tapia (CDT) subproblem that arises in some trust-region algorithms for equality constrained optimization. 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 subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results are also reported.
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