## Mathematical Programming Study, Issues 16-20 |

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### Contents

2 Reduced quasiNewton methods with feasibility improvement | 18 |

3 A superlinearly convergent algorithm for constrained optimization | 60 |

5 A projected Lagrangian algorithm and its implementation for sparse | 84 |

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### Common terms and phrases

active set algorithm Applications approximation assume assumption Banach spaces bounded codes computational conjugate gradient conjugate gradient methods consider constrained optimization constraint qualification convex cone convex program Corollary defined denote derivatives differentiable equality constraints equations equivalent exact penalty function example exists feasible point formula given global Hence Hessian implies inequality constraints infeasible Jacobian Kuhn-Tucker point Lagrange multipliers Lagrangian Lagrangian function Lemma line search linear complementarity problem linear constraints linear programming linearly constrained Lipschitzian manifold Mathematical Programming matrix minimize minimum nonempty nonlinear constraints nonlinear programming objective function obtain optimal solution optimality conditions optimization problems paper penalty function penalty parameter positive definite procedure programming problem Proof Proposition QP sub-problem quadratic programming quasi-Newton method reduced gradient satisfied search direction second order Section sequence solving step length subproblem subset superbasic superlinear convergence Suppose test problems Theorem update vector watchdog technique zero