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  • 1
    Electronic Resource
    Electronic Resource
    Pure adaptive search for finite global optimization (1995)
    Springer
    Mathematical programming 69 (1995), S. 443-448 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; Discrete optimization ; Algorithm complexity ; Random search ; Markov chains
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Pure Adaptive Search is a stochastic algorithm which has been analyzed for continuous global optimization. When a uniform distribution is used in PAS, it has been shown to have complexity which is linear in dimension. We define strong and weak variations of PAS in the setting of finite global optimization and prove analogous results. In particular, for then-dimensional lattice {1,⋯,k} n , the expected number of iterations to find the global optimum is linear inn. Many discrete combinatorial optimization problems, although having intractably large domains, have quite small ranges. The strong version of PAS for all problems, and the weak version of PAS for a limited class of problems, has complexity the order of the size of the range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585570
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Towards Pure Adaptive Search (1995)
    Springer
    Journal of global optimization 7 (1995), S. 93-110 
    Details
    ISSN: 1573-2916
    Keywords: Global optimisation ; stochastic ; random search ; localisation ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The algorithm known as Pure Adaptive Search is a global optimisation ideal with desirable complexity. In this paper we temper it to a framework we term Somewhat Adaptive Search. This retains the desirable complexity, but allows scope for a practical realisation. We introduce a new algorithm termed Pure Localisation Search which attempts to reach the practical ideal. For a certain class of one variable functions the gap is bridged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01100207
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Multidimensional bisection: The performance and the context (1993)
    Springer
    Journal of global optimization 3 (1993), S. 337-358 
    Details
    ISSN: 1573-2916
    Keywords: Bisection ; global optimisation ; branch and bound ; numerical performance ; simplex ; localisation ; deterministic ; mathematical programming ; 90C30 ; 65K05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two aspects of the multidimensional bisection algorithms for the global optimisation of Lipschitz continuous functions are investigated. Firstly, for several test functions we examine the numerical performance of the deepest point algorithm and two acceleration procedures. Secondly, we phrase the branch and bound framework of Horst and Tuy in terms of covers, and show the algorithms to be included in this framework. A result of Basso on the convergence of localisations is extended to higher dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01096775
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    Paper (German National Licenses)
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