The projected gradient method for least squares matrix approximations with spectral constraints. (English) Zbl 0704.65025
A general procedure in using the projected gradient method is described. The projected gradient of the objective function on the manifold of constraints can be formulated explicitly. The explicit form gives rise to the construction of a decent flow that can be followed numerically and also facilitates the computation of the second-order optimality conditions. The procedure can be extended to solve least squares problems for general matrices subject to singular-value constraints.
Reviewer: Shenquan Xie
MSC:
65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
65K05 | Numerical mathematical programming methods |
90C20 | Quadratic programming |