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  • 1
    Electronic Resource
    Electronic Resource
    Homeomorphisms of triangulations with applications to computing fixed points (1981)
    Springer
    Mathematical programming 20 (1981), S. 213-224 
    Details
    ISSN: 1436-4646
    Keywords: Complementary Pivoting Algorithms ; Fixed Points ; Triangulations ; Homeomorphism ; Linearity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In the past decade various complementary pivoting algorithms have been developed to search for fixed points of certain functions and point to set maps. All these methods generate a sequence of simplexes which are ‘shrinking’ to a point. This paper proposes a new method for shrinking the simplexes. It is shown that under certain conditions, the function whose fixed point is sought may be used to control this shrinking process. A computational method for implementing these ideas is also suggested and several examples are solved using this approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589346
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Comparative computer results of a new complementary pivot algorithm for solving equality and inequality constrained optimization problems (1980)
    Springer
    Mathematical programming 18 (1980), S. 169-185 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Equality Constraints ; Fixed Points ; Complementary Pivoting Algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper reports the development of a new algorithm for solving the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints). The approach is based on the complementary pivoting algorithms which have been developed to solve certain classes of fixed point problems. The specific approach is to use the equality constraints to solve for some variables in terms of the remaining ones thus enabling one to eliminate the equality constraints altogether. The result, under certain circumstances, is an optimization problem which may be transformed into a fixed point problem in such a way that a complementary pivoting code may be used to search for a solution. Seventeen test problems have been solved by this method and the results are compared against those obtained from GRG (Generalized Reduced Gradient method). The results of the tests indicate that the fixed point approach is robust (all 17 problems were solved by this method where as GRG solved 16). As to the computer times, the fixed point code proved to be as fast or faster than GRG on the lower dimensional problems; however, as the dimension increased, the trend reversed and on a 40 dimensional problem GRG was approximately 11 times faster. The conclusion from these tests is that when the dimension of the original problem can be reduced sufficiently by the equality constraints, the fixed point approach appears to be more effective than GRG.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588312
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    The effectiveness of finite improvement algorithms for finding global optima (1993)
    Springer
    Mathematical methods of operations research 37 (1993), S. 257-272 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper investigates the effectiveness of using finite improvement algorithms for solving decision, search, and optimization problems. Finite improvement algorithms operate in a finite number of iterations, each taking a polynomial amount of work, where strict improvement is required from iteration to iteration. The hardware, software, and way of measuring complexity found in the polynomial setting are modified to identify the concept of repetition and define the new classes of decision problems,FI andNFI. A firstNFI-complete problem is given using the idea ofFI-transformations. Results relating these new classes toP, NP, andNP-complete are given. It is shown that if an optimization problem in a new classPGS isNP-hard, thenNP=co-NP. TwoPGS problems are given for which no polynomial algorithms are known to exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415994
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    An analysis and implementation of an efficient in-place bucket sort (1997)
    Springer
    Acta informatica 34 (1997), S. 687-700 
    Details
    ISSN: 1432-0525
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract. Various methods, such as address-calculation sorts, distribution counting sorts, radix sorts, and bucket sorts, use the values of the numbers being sorted to increase efficiency but do so at the expense of requiring additional storage space. In this paper, a specific implementation of bucket sort is presented whose primary advantanges are that (i) linear average-time performance is achieved with an additional amount of storage equal to any fraction of the number of elements being sorted and (ii) no linked-list data structures are used (all sorting is done with arrays). Analytical and empirical results show the trade-off between the additional storage space used and the improved computational efficiency obtained. Computer simulations show that for lists containing 1,000 to 30,000 uniformly distributed positive integers, the sort developed here is faster than both Quicksort and a standard implementation of bucket sort. Furthermore, the running time increases with size at a slower rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002360050103
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    Paper (German National Licenses)
    Fulltext
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