Projection Methods in Constrained Optimisation and Applications to Optimal Policy Decisions |
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Projection Methods in Constrained Optimisation and Applications to Optimal ... Berc Rustem No preview available - 2014 |
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active constraints active set approximation arg min Chapter columns computed condition constrained optimisation constrained problem constraint normals convex corresponding current optimal d₁ denotes descent direction discussed in Section equality constraints f(xx feasible point feasible region G(xx G₁ Gauss-Newton algorithm Gill and Murray given Goldfarb gradient Hence Hessian matrix Hk Nm inequality constraints intersection iteration Lagrange multipliers Lemma linearly constrained linearly independent minimisation nonlinear constraints nonlinear programming objective function obtained optimal trajectory optimisation problem optimum Ortega and Rheinboldt Polak policy optimisation positive definite Powell projection algorithm projection methods projection operator quadratic function quadratic objective function quadratic programming Quasi-Newton Methods rate of convergence respecification Rheinboldt 1970 Rustem satisfied second derivative sequence solving Step steplength stepsize strategies subproblems subspace Theorem updating formula values vector vf xx vf(x vf(xx violated constraint xk+1 xx+1 Zarrop ак тк