10 research outputs found

    H\"older Error Bounds and H\"older Calmness with Applications to Convex Semi-Infinite Optimization

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    Using techniques of variational analysis, necessary and sufficient subdifferential conditions for H\"older error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the H\"older calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the H\"older calmness modulus of the argmin mapping in the framework of linear programming.Comment: 25 page

    Intelligent Computing: The Latest Advances, Challenges and Future

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    Computing is a critical driving force in the development of human civilization. In recent years, we have witnessed the emergence of intelligent computing, a new computing paradigm that is reshaping traditional computing and promoting digital revolution in the era of big data, artificial intelligence and internet-of-things with new computing theories, architectures, methods, systems, and applications. Intelligent computing has greatly broadened the scope of computing, extending it from traditional computing on data to increasingly diverse computing paradigms such as perceptual intelligence, cognitive intelligence, autonomous intelligence, and human-computer fusion intelligence. Intelligence and computing have undergone paths of different evolution and development for a long time but have become increasingly intertwined in recent years: intelligent computing is not only intelligence-oriented but also intelligence-driven. Such cross-fertilization has prompted the emergence and rapid advancement of intelligent computing. Intelligent computing is still in its infancy and an abundance of innovations in the theories, systems, and applications of intelligent computing are expected to occur soon. We present the first comprehensive survey of literature on intelligent computing, covering its theory fundamentals, the technological fusion of intelligence and computing, important applications, challenges, and future perspectives. We believe that this survey is highly timely and will provide a comprehensive reference and cast valuable insights into intelligent computing for academic and industrial researchers and practitioners

    Intelligent computing : the latest advances, challenges and future

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    Computing is a critical driving force in the development of human civilization. In recent years, we have witnessed the emergence of intelligent computing, a new computing paradigm that is reshaping traditional computing and promoting digital revolution in the era of big data, artificial intelligence and internet-of-things with new computing theories, architectures, methods, systems, and applications. Intelligent computing has greatly broadened the scope of computing, extending it from traditional computing on data to increasingly diverse computing paradigms such as perceptual intelligence, cognitive intelligence, autonomous intelligence, and human computer fusion intelligence. Intelligence and computing have undergone paths of different evolution and development for a long time but have become increasingly intertwined in recent years: intelligent computing is not only intelligence-oriented but also intelligence-driven. Such cross-fertilization has prompted the emergence and rapid advancement of intelligent computing

    Error Bound for Conic Inequality in Hilbert Spaces

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    We consider error bound issue for conic inequalities in Hilbert spaces. In terms of proximal subdifferentials of vector-valued functions, we provide sufficient conditions for the existence of a local error bound for a conic inequality. In the Hilbert space case, our result improves and extends some existing results on local error bounds

    Stable well-posedness and tilt stability with respect to admissible functions

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    Note that the well-posedness of a proper lower semicontinuous function f can be equivalently described using an admissible function. In the case when the objective function f undergoes the tilt perturbations in the sense of Poliquin and Rockafellar, adopting admissible functions ϕ and ψ, this paper introduces and studies the stable well-posedness of f with respect to ϕ (in brief, ϕ-SLWP) and tilt-stable local minimum of f with respect to ψ (in brief, ψ-TSLM). In the special case when ϕ(t) = t2 and ψ(t) = t, the corresponding ϕ-SLWP and ψ-TSLM reduce to the stable second order local minimizer and tilt stable local minimum respectively, which have been extensively studied in recent years. We discover an interesting relationship between two admissible functions ϕ and ψ: ψ(t) = (ϕ′)-1(t), which implies that a proper lower semicontinuous function f on a Banach space has ϕ-SLWP if and only if f has ψ-TSLM. Using the techniques of variational analysis and conjugate analysis, we also prove that the strong metric ϕ′-regularity of ∂f is a sufficient condition for f to have ϕ-SLWP and that the strong metric ϕ′-regularity of ∂ [co(f + δBX [ x,r ]) ] for some r> 0 is a necessary condition for f to have ϕ-SLWP. In the special case when ϕ(t) = t2, our results cover some existing main results on the tilt stability

    Variational principles on topological spaces

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    Isolated Calmness and Sharp Minima via Hölder Graphical Derivatives

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    The paper utilizes Hölder graphical derivatives for characterizing Hölder strong subregularity, isolated calmness and sharp minimum. As applications, we characterize Hölder isolated calmness in linear semi-infinite optimization and Hölder sharp minimizers of some penalty functions for constrained optimization.The research of the first and second authors was supported by the Australian Research Council, project DP160100854. The first author benefited from the support of the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie Grant Agreement No. 823731 CONMECH. The research of the second author was also supported by MINECO of Spain and FEDER of EU, grant MTM2014-59179-C2-1-P. The research of the third author was supported by the Research Grants Council of Hong Kong (RGC Ref No. 15216518). The research of the fourth author was supported by the National Natural Science Foundation of China, grants 11801497 and 11771384

    Defining honeybee subspecies in an evolutionary context warrants strategized conservation

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    Despite the urgent need for conservation consideration, strategic action plans for the preservation of the Asian honeybee, Apis cerana Fabricius, 1793, remain lacking. Both the convergent and divergent adaptations of this widespread insect have led to confusing phenotypical traits and inconsistent infraspecific taxonomy. Unclear subspecies boundaries pose a significant challenge to honeybee conservation efforts, as it is difficult to effectively prioritize conservation targets without a clear understanding of subspecies identities. Here, we investigated genome variations in 362 worker bees representing almost all populations of mainland A. cerana to understand how evolution has shaped its population structure. Whole-genome single nucleotide polymorphisms (SNPs) based on nuclear sequences revealed eight putative subspecies, with all seven peripheral subspecies exhibiting mutually exclusive monophyly and distinct genetic divergence from the widespread central subspecies. Our results demonstrated that most classic morphological traits, including body size, were related to the climatic variables of the local habitats and did not reflect the true evolutionary history of the organism. Thus, such morphological traits were not suitable for subspecific delineation. Conversely, wing vein characters showed relative independence to the environment and supported the subspecies boundaries inferred from nuclear genomes. Mitochondrial phylogeny further indicated that the present subspecies structure was a result of multiple waves of population divergence from a common ancestor. Based on our findings, we propose that criteria for subspecies delineation should be based on evolutionary independence, trait distinction, and geographic isolation. We formally defined and described eight subspecies of mainland A. cerana. Elucidation of the evolutionary history and subspecies boundaries enables a customized conservation strategy for both widespread and endemic honeybee conservation units, guiding colony introduction and breeding
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