In this paper, an active set smoothing function based on the plus function is constructed for the maximum function. The active set strategy used in the smoothing function reduces the number of gradients and Hessians evaluations of the component functions in the optimization. Combing the active set smoothing function, a simple adjustment rule for the smoothing parameters, and an unconstrained minimization method, an active set smoothing method is proposed for solving unconstrained minimax problems. The active set smoothing function is continuously differentiable, and its gradient is locally Lipschitz continuous and strongly semismooth. Under the boundedness assumption on the level set of the objective function, the convergence of the proposed method is established. Numerical experiments show that the proposed method is feasible and efficient, particularly for the minimax problems with very many component functions.
With the development of rural tourism, rural culture in China has suffered from development problems. Existing studies focus more on how to protect rural culture, ignoring the dynamic changes in rural culture. Therefore, cultural memory offers an important perspective to review the dynamic process of cultural changes. This paper uses the concept of cultural landscape to explore the changes in rural culture from the perspective of cultural memory. The research methods of historical data analysis and field investigation are used. The change process of the cultural landscape in Anzhen Village is explored. Firstly, the clan-style group life in the traditional human–land relationship is the germination of cultural memory. Secondly, typical Chongqing residential mansions become ways of spatial expression of the local cultural landscape. Thirdly, the group interpretation of the settlement landscape becomes the continuation of local memory. Fourthly, the migration of living settlements in the dual influence of modern transportation and administrative divisions is the deconstruction of local memory. Fifthly, the touristic reconstruction of the traditional cultural landscape is summarized as memory reconstruction. In addition, the factors affecting the changes in the cultural landscape are analyzed from both internal and external aspects. The discussion on the dynamic changes in the cultural landscape provides a theoretical and practical basis for the analysis, protection, and inheritance of rural culture.
Freeform optics are defined as nonrotational symmetric optical surfaces in the manufacturing industry. Freeform optics are extensively applied to many areas in order to improve system performance. Fast tool servo (FTS) assisting single-point diamond turning technology has high application prospects in freeform optics machining. This paper discusses the interpolation algorithm for tool path generation of FTS through the application of a radial basis function (RBF) algorithm. For this purpose, a positive definite RBF with compact support was employed as the interpolant. The existence is mathematically proven. Numerical simulations were performed to compare the performances of the RBF algorithm and commonly used algorithms for satisfying the requirements of existence, smoothness, and accuracy. Machining experiments were also conducted to validate the applicability of the algorithm. The simulation results showed that the RBF interpolation algorithm outperformed other algorithms in terms of smoothness. The RBF algorithm also provided the highest interpolation accuracy. Furthermore, the RBF interpolation algorithm exhibited the highest accuracy for error distribution, with large errors distributed mainly in transition areas. The machining results were also in general agreement with the simulation results although obvious practical errors were observed. Overall, RBF interpolation can provide higher accuracy and better smoothness in the tool path generation of FTS.
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