Partial Lagrangian relaxation for the unbalanced orthogonal Procrustes problem

Yong Xia () and Ying-Wei Han ()

Mathematical Methods of Operations Research, 2014, vol. 79, issue 2, 225-237

Abstract: Based on a novel reformulation of the feasible region, we propose and analyze a partial Lagrangian relaxation approach for the unbalanced orthogonal Procrustes problem (UOP). With a properly selected Lagrangian multiplier, the Lagrangian relaxation (LR) is equivalent to the recent matrix lifting semidefinite programming relaxation (MSDR), which has much more variables and constraints. Numerical results show that (LR) is solved more efficiently than (MSDR). Moreover, based on the special structure of (LR), we successfully employ the well-known Frank–Wolfe algorithm to efficiently solve very large instances of (LR). The rate of the convergence is shown to be independent of the row-dimension of the matrix variable of (UOP). Finally, motivated by (LR), we propose a Lagrangian heuristic for (UOP). Numerical results show that it can efficiently find the global optimal solutions of some randomly generated instances of (UOP). Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Orthogonal Procrustes problem; Lagrangian relaxation; Semidefinite programming; Quadratic conic programming; Frank–Wolfe algorithm; 90C20; 90C22 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00186-013-0460-7

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