Abstract
We propose an index search method (ISM) for solving nonnegative least squares problems (NNLS). This method uses inner and outer schemes to find the index set corresponding to the nonzero component of the optimal solution. The outer iteration updates the approximate index set such that the objective value of the sequence generated by ISM is monotonically decreasing. Hence, the index set generated by ISM does not repeat, and the optimal solution can be achieved with finite iteration steps. Some normal equations need to be solved in the inner iteration, which is the dominant computational complexity in ISM. Numerical experiments are provided to support the theoretical results.
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