## Trust region strategies for unconstrained and constrained minimization |

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### Contents

The Unconstrained Problem ll | 11 |

The Implementation of the Unconstrained Algorithm | 52 |

The Constrained Problem | 68 |

Copyright | |

2 other sections not shown

### Common terms and phrases

algorithm 2.II assume Ax,Av Ax(A Ax(X B+XI BFGS update Bk+l Chapter completes the proof compute condition number constrained minimization convergence test convex defined descent direction dN3dNV Euclidean norm full rank global convergence guarantee HddlHd Hessian matrix implies inequality INI3d L(x,v+Av Lagrange multipliers Lagrangian Lagrangian function lemma line search matrix norms Newton step norm obtain orthogonal matrix penalty function permutation matrix PL(x positive definite problem Q-R decomposition q-superlinear convergence quadratic approximation quadratic function radius satisfies solution solve steepest descent Taylor's theorem theorem 2.l5 trust region strategy UI UJ UJ UJ unconstrained upper triangular v+Av v+Av(X vector Vf(x Vf(x+s Vf(xk+l Vh(x VxL(x,v X1XN xk-x xk+l xk+l-x zero