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PROJECTION METHODS FOR COMPUTING
AN ALGORITHM FOR POSITIVE DEFINITE
9 other sections not shown
active constraints active set approximation Chapter Cholesky factors chosen column computed condition constrained optimisation constrained problem constraint normals convex corresponding defined denotes descent direction desired trajectories discussed in Section elements equality constraints feasible point feasible region follows Gauss-Newton algorithm Gill and Murray given Goldfarb gradient Hence inequality constraints intersection iteration Lagrange multipliers Lemma linear inequality Linearly Constrained linearly independent minimisation nonlinear constraints nonlinear programming objective function obtained optimal solution optimisation problem optimum Ortega and Rheinboldt P[Hk Polak policy instruments policy optimisation Powell projection algorithm projection methods projection operator Proof quadratic approximation quadratic function quadratic objective function quadratic programming Quasi-Newton Methods rate of convergence respecification result Rheinboldt 1970 Rustem satisfied sequence solving Step steplength stepsize strategies subproblem subspace Theorem 4.9 updating formula vector vf(x vf(xk violated constraint weighting matrix Zarrop zero