## A Conjugate Gradient Method for Nonlinear Programming |

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### Contents

THEORETICAL BASIS OF CONJUGATE | 17 |

COMPUTATIONAL ASPECTS | 77 |

CHEMICAL ENGINEERING APPLICATIONS | 85 |

2 other sections not shown

### Common terms and phrases

assumed Chapter chemical engineering chemical equilibrium concave function conjugate gradient algorithm conjugate gradient method conjugate-gradient algorithm constrained global maximum constraint basis convex dimensional equality constraints Euclidean projection operator Euclidean space finite number Fletcher and Powell formulated functional evaluations g(xQ given by equation gradient direction gradient projection method Hessian matrix initial feasible point intersection of q inverse Lagrange multipliers linear constraints linear inequality linear manifold linear programming linearly independent matrix H matrix of second matrix operator mutually conjugate directions necessary and sufficient Newton's method nonlinear programming problem objective function obtained operator H optimal control orthogonal procedure proof of Theorem q hyperplanes q linearly q q-1 q q q-i q qq q-i q quadratic function quadratic programming algorithm quadratic programming problem quadratically convergent recursion relations Rosen's gradient projection Rosen's method second partial derivatives solve steepest-ascent subspace sufficient conditions technique test problem unconstrained maximization unit normals variables vector