Towards global optimisation: proceedings of a workshop at the University of Cagliari, Italy, October 1974, Volume 1
Laurence Charles Ward Dixon, G. P. Szegö
North-Holland Pub. Co., 1975 - Mathematics - 472 pages
Global optimisation; Unconstrained optimization; Constrained optimisation; Dynamic systems.
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Paper 1 THE PRACTICE OF OPTIMISATION
Paper 2 TOWARDS GLOBAL OPTIMISATION
THE USE OF REGIONS OF ATTRACTION
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applied approach approximation assume assumptions asymptotically stable bounded Branin condition number consider constant constraints convex critical point defined derivatives determine differential equation dimensional eigenvalue ellipse evaluations exists formula function f function value G Treccani given global minimum global optimisation grad J(u Hatfield Polytechnic hence Hessian matrix identified implies Lemma level set Liapunov function linear search located Mathematics metric space minima minimisation algorithm minimum point neighbourhood nonlinear objective function obtained optimum paper parameters penalty function positive definite proof properties quadratic function quadratic termination Quasi-Newton methods random search rate of convergence region of attraction right maximal solution Rosenbrock function routine saddle point satisfy search directions second order convergence sequence solving space Spedicato starting point stationary point step stochastic Szego technique THEOREM Let trajectory update Variable Metric Method vector weak right maximal weakly positively invariant zero