In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
An extension of the global convergence framework for unconstrained derivative-free op- timization methods is presented.The extension makes it possible for the framework to include opti- mization methods with varying c...An extension of the global convergence framework for unconstrained derivative-free op- timization methods is presented.The extension makes it possible for the framework to include opti- mization methods with varying cardinality of the ordered direction set.Grid-based search methods are shown to be a special case of the more general extended global convergence framework.Furthermore, the required properties of the sequence of ordered direction sets listed in the definition of grid-based methods are relaxed and simplified by removing the requirement of structural equivalence.展开更多
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
文摘An extension of the global convergence framework for unconstrained derivative-free op- timization methods is presented.The extension makes it possible for the framework to include opti- mization methods with varying cardinality of the ordered direction set.Grid-based search methods are shown to be a special case of the more general extended global convergence framework.Furthermore, the required properties of the sequence of ordered direction sets listed in the definition of grid-based methods are relaxed and simplified by removing the requirement of structural equivalence.
