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A block decomposition method is proposed for minimizing a (possibly non-convex)
continuously differentiable function subject to one linear equality constraint and
simple bounds on the variables. The proposed method iteratively selects a pair of
coordinates according to an almost cyclic strategy that does not use first-order information,
allowing us not to compute the whole gradient of the objective function during
the algorithm. Using first-order search directions to update each pair of coordinates,
global convergence to stationary points is established for different choices of the stepsize
under an appropriate assumption on the level set. In particular, both inexact and
exact line search strategies are analyzed. Further, linear convergence rate is proved
under standard additional assumptions. Numerical results are finally provided to show
the effectiveness of the proposed method
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