## Superlinearly Convergent Algorithms in Nonlinear Programming |

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### Contents

Definitions of Convergence Rate | 2 |

An Upper Bound | 16 |

Convergence Rates for Some | 22 |

7 other sections not shown

### Common terms and phrases

Algorithm for Nonlinear algorithm for solving Assume Cauchy sequence compact set completes the proof concave constrained problems Convergence and convergence convergence of algorithm convergence rate convergence theorem convex programming defined denote Equations and Inequalities feasible point Frobenius norm g and h global algorithm global convergence globally superlinearly convergent gradient holds implies Kuhn Kuhn-Tucker point Lemma Linear independence linear programming linear system Lipschitz continuity lower bound lower semicontinuous modified algorithm modified Lagrangian Newton's method nonlinear programming O.L. Mangasarian objective function Ortega and Rheinboldt pe[l perturbed subproblem point of 1.1 positive definite Powell problem 1.1 programming problem Pshenichnyi quadratic programming Quasi-Newton methods R-linear R-sublinear rate of convergence rithm Robinson root convergence factor satisfied sequence in Rn solution solving 1.1 Starting point stepsize methods sublinear sufficient condition sufficient criteria superlinear convergence SUPERLINEARLY CONVERGENT ALGORITHMS T.J. Huang Tucker point variable metric algorithms vectors Wilson's algorithm x6Rn xeRn