A nontangential cutting plane algorithm
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The cutting plane algorithm typically generates cuts that are tangential, or nearly so, to the Lagrangian dual function of the underlying optimization problem. This paper demonstrates that the algorithm still converges to an optimal solution when cuts are nontangential. These cuts are generated by not solving the subproblems to optimality or nearly so. Computational results from randomly generated linear and quadratic programming problems indicate that nontangential cuts can lead to a more efficient algorithm.