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An algorithm using quadratic interpolation for unconstrained derivative free optimization

An algorithm using quadratic interpolation for unconstrained derivative free optimization,A. R. Conn,P. L. Toint

An algorithm using quadratic interpolation for unconstrained derivative free optimization   (Citations: 44)
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Published in 1996.
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    • ...The general structure of UOBYQA follows a model-based approach [4, 5], which constructs a chain of local quadratic models that approximate the objective function...
    • ...A general framework of this approach is given by Conn and Toint in [5], and convergence analysis is presented in [4]...

    Geng Denget al. Variable-Number Sample-Path Optimization

    • ...The general structure of UOBYQA follows a model-based approach (Conn and Toint 1996), which constructs a chain of local quadratic models to approximate the objective function within certain trust regions (Nocedal and Wright 2006)...

    Punit Prakashet al. Design optimization of a robust sleeve antenna for hepatic microwave a...

    • ...For the purpose of reducing computation time, Conn et al. [5] proposed to use Newton fundamental polynomial function for constructing the model...
    • ...S for reducing the value k'( ˆ X)¡1k by some suitable method (see [5] for details)...
    • ...Conn and Toint claim that the model-based algorithm is robust for small errors in objective function from numerical results in [5, 7], in which the errors was generated in uniformly random number...

    Jun TAKAKI. A Derivative-Free Trust-Region Algorithm for Unconstrained Optimizatio...

    • ...There is also a related class of “global modeling methods” that use design of interpolation models [1,6,7]...

    S. Z. Hassanet al. Quadratic Interpolation Algorithm for Minimizing Tabulated Function

    • ... approximate the objective function locally and hence are likely to approximate it better than a global model would, they are generated using a relatively small number of points (relevant for expensive functions), they are efficiently minimized by gradient-based algorithms and they retain their goodness in the presence of noise thanks to the interpolation technique used and since, being quadratic, they smooth out noise fluctuations [3, 10, ...
    • ...The quadratic model functions are generated by interpolation [8, 10, 33, 42, 43]...
    • ...A linear polynomial was found to be inferior to a quadratic one [32, 34], while polynomials of degree higher than two [10] were rejected since they may require more interpolation points which is undesirable when function evaluations are expensive, and since they may contain oscillations [3]...

    Yoel Tenneet al. A Memetic Algorithm Using a Trust-Region Derivative-Free Optimization ...

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