"An Inexact Newton Method for Nonconvex Equality Constrained Optimization"
R. Byrd, F. Curtis, J. Nocedal.
Mathematical Programming, DOI: 10.1007/s10107-008-0248-3 (2007).

We present a matrix-free line search algorithm for large-scale equality con- strained optimization that allows for inexact step computations. For strictly con- vex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd, Curtis, and Nocedal [2]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal-dual iteration matrix. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. The complete algorithm is characterized by its emphasis on su±cient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.
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