Quadratic regularization projected alternating Barzilai–Borwein method for constrained optimization

In this paper, based on the regularization techniques and projected gradient strategies, we present a quadratic regularization projected alternating Barzilai–Borwein (QRPABB) method for minimizing differentiable functions on closed convex sets. We show the convergence of the QRPABB method to a constrained stationary point for a nonmonotone line search. When the objective function is convex, we prove the error in the objective function at iteration k is bounded by a k+1 for some a independent of k. Moreover, if the objective function is strongly convex, then the convergence rate is R-linear. Numerical comparisons of methods on box-constrained quadratic problems and nonnegative matrix factorization problems show that the QRPABB method is promising.