# PQN

June 2010

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## Summary

PQN implements a limited-memory projected quasi-Newton algorithm for constrained optimization. It uses L-BFGS updates to build a diagonal plus low-rank quadratic approximation to the function, uses the spectral projected gradient (SPG) algorithm to minimize the quadratic approximation subject to the constraints present in the original problem, and uses a backtracking line search to generate new parameter vectors satisfying an Armijo-like sufficient decrease condition. The method is most effective when computing the projection onto the constraint set can be done much more efficiently than evaluating the function.