## Mathematical Programming Study, Volumes 16-18 |

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### Contents

2 Reduced quasiNewton methods with feasibility improvement | 18 |

3 A superlinearly convergent algorithm for constrained optimization | 45 |

4 Computation of the search direction in constrained optimization | 62 |

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21 other sections not shown

### Common terms and phrases

algorithm applied approximation assume assumptions augmented Lagrangian bounded codes computational conjugate gradient methods constrained optimization convex Corollary defined denote derivatives descent direction differentiable dp(u equality constraints equations exact penalty function exists exterior penalty feasible point finite given hence Hessian inequality constraints infeasible Jacobian matrix Kuhn-Tucker point Lagrange multipliers Lagrangian function Lemma line search linear constraints linearly constrained Lipschitz continuous Lipschitzian major iteration manifold Mathematical Programming minimize nonlinear constraints nonlinear programming objective function obtained optimal solution optimality conditions optimization problems original problem paper penalty function penalty parameter piecewise smooth function positive definite procedure Proof Proposition QP sub-problem quadratic programming quasi-Newton method rate of convergence reduced gradient reduced problem satisfied search direction second order Section sequence smooth functions solving step length subproblem superbasic superlinear convergence test problems Theorem update variable metric vector W(xk watchdog technique zero