Abstract
Newton type algorithms have been widely studied for nonlinearly constrained problems in connection with exact penalty functions, but essentially with the hypothesis that the approximation of the Hessian of the Lagrangian is positive definite. This excludes Newton's method for nonconvex problems. Assuming the linear independence of the gradients of active constraints, under a weak second-order sufficiency condition, we prove the quadratic convergence of Newton's method without any strict complementarity hypothesis and we prove that (locally) the exact penalty function decreases in Newton's direction.
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© 1989 Springer Verlag
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Bonnans, J.F. (1989). Local study of newton type algorithms for constrained problems. In: Dolecki, S. (eds) Optimization. Lecture Notes in Mathematics, vol 1405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083583
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DOI: https://doi.org/10.1007/BFb0083583
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