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Projection Algorithms for Non-Convex Minimization with Application to Sparse Principal Component Analysis
We consider concave minimization problems over non-convex sets.Optimization
problems with this structure arise in sparse principal component analysis. We
analyze both a gradient projection algorithm and an approximate Newton
algorithm where the Hessian approximation is a multiple of the identity.
Convergence results are established. In numerical experiments arising in sparse
principal component analysis, it is seen that the performance of the gradient
projection algorithm is very similar to that of the truncated power method and
the generalized power method. In some cases, the approximate Newton algorithm
with a Barzilai-Borwein (BB) Hessian approximation can be substantially faster
than the other algorithms, and can converge to a better solution