Projection Methods in Constrained Optimisation and Applications to Optimal Policy Decisions |
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Page 136
... stepsize rule that requires the projection of the unconstrained step for each test value of the stepsize ( see Section ( 4.1.2 ) ) . The determination of the stepsize is simplified in algorithm ( 4.1.7 ) by dividing this process into ...
... stepsize rule that requires the projection of the unconstrained step for each test value of the stepsize ( see Section ( 4.1.2 ) ) . The determination of the stepsize is simplified in algorithm ( 4.1.7 ) by dividing this process into ...
Page 156
... Stepsize Strategies тк in The stepsizes ак in the unconstrained step ( 4.1.11 ) and xk + 1 = xx + Tk ( xp - xx ) ( 4.2.1 ) determine the convergence of algorithm ( 4.1.7 ) . The 156 Convergence of the Algorithm Stepsize Strategies.
... Stepsize Strategies тк in The stepsizes ак in the unconstrained step ( 4.1.11 ) and xk + 1 = xx + Tk ( xp - xx ) ( 4.2.1 ) determine the convergence of algorithm ( 4.1.7 ) . The 156 Convergence of the Algorithm Stepsize Strategies.
Page 163
... stepsize strategies ( 4.2.21 ) and ( 4.2.26 ) below avoid the computation of new . projection subproblems for each value of the step size . size ak direction The following result establishes a lower bound on the step if it is intended ...
... stepsize strategies ( 4.2.21 ) and ( 4.2.26 ) below avoid the computation of new . projection subproblems for each value of the step size . size ak direction The following result establishes a lower bound on the step if it is intended ...
Contents
Chapter | 3 |
PROJECTION METHODS FOR COMPUTING | 43 |
QUADRATIC PROGRAMMING | 76 |
Copyright | |
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Projection Methods in Constrained Optimisation and Applications to Optimal ... Berc Rustem No preview available - 2014 |
Common terms and phrases
active constraints active set approximation arg min Chapter Cholesky factors columns computed condition constrained optimisation constrained problem constraint normals convergence convex corresponding current optimal d₁ denotes descent direction discussed in Section equality constraints f(xx feasible point feasible region G₁ Gauss-Newton algorithm Gill and Murray given Goldfarb gradient Hence 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 instruments policy optimisation positive definite Powell projection algorithm projection methods quadratic function quadratic objective function quadratic programming Quasi-Newton Methods rate of convergence respecification Rheinboldt 1970 Rustem satisfied second derivative sequence solving Step stepsize strategies subproblems subspace Theorem 4.9 updating formula values vector vf xx vf(x vf(xx violated constraint xk+1 xx+1 Zarrop ак тк