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
We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and e...We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.展开更多
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
We discuss a filter-based pattern search method for unconstrained optimization in this paper. For the purpose to broaden the search range we use both filter technique and frames, which are fragments of grids, to provi...We discuss a filter-based pattern search method for unconstrained optimization in this paper. For the purpose to broaden the search range we use both filter technique and frames, which are fragments of grids, to provide a new criterion of iterate acceptance. The convergence can be ensured under some conditions. The numerical result shows that this method is practical and efficient.展开更多
Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, econ...Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we introduced an integer m in the algorithm which controls the number of steps of iteration update. We mean along the descent direction to allow the algorithm to?go ahead m steps at most to explore whether we can get better solution further. The experiment proved the strategy’s efficiency.展开更多
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.
文摘We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.
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We discuss a filter-based pattern search method for unconstrained optimization in this paper. For the purpose to broaden the search range we use both filter technique and frames, which are fragments of grids, to provide a new criterion of iterate acceptance. The convergence can be ensured under some conditions. The numerical result shows that this method is practical and efficient.
文摘Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we introduced an integer m in the algorithm which controls the number of steps of iteration update. We mean along the descent direction to allow the algorithm to?go ahead m steps at most to explore whether we can get better solution further. The experiment proved the strategy’s efficiency.
基金supported by National Natural Science Foundation of China(No.11171159)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD) of ChinaCNPq of Brazil
