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- W2106173883 abstract "This paper considers optimization problems on the Stiefel manifold $$X^{mathsf{T}}X=I_p$$ , where $$Xin mathbb {R}^{n times p}$$ is the variable and $$I_p$$ is the $$p$$ -by- $$p$$ identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of $$X$$ and the null space of $$X^{mathsf{T}}$$ . While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai–Borwein-like method under the new update scheme. The global convergence of the method is established with an adaptive nonmonotone line search. The numerical tests on the nearest low-rank correlation matrix problem, the Kohn–Sham total energy minimization and a specific problem from statistics demonstrate the efficiency of the new method. In particular, the new method performs remarkably well for the nearest low-rank correlation matrix problem in terms of speed and solution quality and is considerably competitive with the widely used SCF iteration for the Kohn–Sham total energy minimization." @default.
- W2106173883 created "2016-06-24" @default.
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- W2106173883 date "2014-09-17" @default.
- W2106173883 modified "2023-10-16" @default.
- W2106173883 title "A framework of constraint preserving update schemes for optimization on Stiefel manifold" @default.
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- W2106173883 doi "https://doi.org/10.1007/s10107-014-0816-7" @default.
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