A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints

A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to simple bounds and linear equality constraints. The method alternates between a classical primal-dual step and a Newton-like modified barrier step in order to ensure descent on a suitable merit function. Convergence of a well-defined subsequence of iterates is proved from arbitrary starting points. Preliminary numerical results are presented.

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