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A subspace version of the Wang-Yuan augmented Lagrangian-trust region method for equality constrained optimization. (English) Zbl 1472.90127

Summary: Subspace properties are presented for the trust-region subproblem that appears in the Augmented Lagrangian-Trust-Region method recently proposed by X. Wang and Y. Yuan [Optim. Methods Softw. 30, No. 3, 559–582 (2015; Zbl 1325.90091)]. Specifically, when the approximate Lagrangian Hessians are updated by suitable quasi-Newton formulas, we show that any solution of the corresponding \(k\)th subproblem belongs to the subspace spanned by all gradient vectors of the objective and of the constraints computed up to iteration \(k\). From this result, a subspace version of the referred method is proposed for large-scale equality constrained optimization problems. The subspace method is suitable to problems in which the number of constraints is much lower than the number of variables.

MSC:

90C30 Nonlinear programming
90C55 Methods of successive quadratic programming type

Citations:

Zbl 1325.90091

Software:

ALGENCAN; minpack; GQTPAR
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Full Text: DOI

References:

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