## Nonlinear programming, 2: proceedings of the Special Interest Group on Mathematical Programming symposium, conducted by the Computer Sciences Department at the University of Wisconsin--Madison, April 15-17, 1974Association for Computing Machinery. Special Interest Group on Mathematical Programming, University of Wisconsin--Madison. Computer Sciences Dept Convergence properties of a class of minimization algorithms; Convergence of the reduced gradient method; A quasi-newton method for unconstrained minimization problems; Superlinearly convergent algorithms for linearly constrained optimization; An ideal penalty function for constrained optimization; On penalty and multiplier methods for constrained minimization; Rate of convergence of the method of multipliers with inexact minimization; Optimization with corners; The use of matrix factorizations in derivative-free nonlinear least squares algorithms; Newton derived methods for nonlinear equations and inequalities; Disjunctive programming: cutting planes from logical conditions. |

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### Contents

Convergence of the Reduced Gradient Method | 29 |

A QuasiNewton Method for Unconstrained Minimization Problems | 55 |

Superlinearly Convergent Algorithms for Linearly Constrained Optimization | 101 |

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algorithm applied approximation assume assumptions augmented Lagrangian bounded Branch and Bound coefficients column Compute condition constraints continuously differentiable Convex Programming criterion cutting planes defined denote disjunctive equation feasible finite number follows formula g_(k given global convergence Gomory Gradient method h e H Hence Hessian matrix Hestenes hyperplane i e Q implies inexact minimization infinite Integer Programming iteration Lagrange multiplier Lagrangian Lemma linear programming Lipschitz Lipschitz continuous matrix maximizing method of multipliers minimum multiplier method Nonlinear Programming objective function obtain optimal solution parameters penalty function penalty method pivot row positive definite Powell Powell/Hestenes procedure programming problem Proof quadratic quasi-Newton method rate of convergence Rockafellar round-off satisfied second derivative sequence solve stationary point sufficiently large tableau Taylor's theorem Theorem tion unconstrained minimization updating vector Vf(x zero zero-one zero-one