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  • 1
    Electronic Resource
    Electronic Resource
    A dual method for discrete Chebychev curve fitting (1980)
    Springer
    Mathematical programming 19 (1980), S. 186-199 
    Details
    ISSN: 1436-4646
    Keywords: Regression ; Curve Fitting ; Min—Max ; Chebychev
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a special purpose dual algorithm for obtaining a Chebychev approximation to an overdetermined system of linear equations. The method is founded on the principles of linear programming and is designed to take advantage of the problem's special structure. It is shown that, while maintaining a reduced basis, certain iterations of the standard dual algorithm may be combined into one. Two computer code implementations of the method are discussed and a computational comparison with another algorithm for Chebychev approximation is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581640
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  • 2
    Electronic Resource
    Electronic Resource
    Strongly polynomial dual simplex methods for the maximum flow problem (1998)
    Springer
    Mathematical programming 80 (1998), S. 17-33 
    Details
    ISSN: 1436-4646
    Keywords: Dual simplex method ; Maximum flow ; Strongly polynomial ; Preflow algorithm ; Valid distance labels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents dual network simplex algorithms that require at most 2nm pivots and O(n 2 m) time for solving a maximum flow problem on a network ofn nodes andm arcs. Refined implementations of these algorithms and a related simplex variant that is not strictly speaking a dual simplex algorithm are shown to have a complexity of O(n 3). The algorithms are based on the concept of apreflow and depend upon the use of node labels that are underestimates of the distances from the nodes to the sink node in the extended residual graph associated with the current flow. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582129
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  • 3
    Electronic Resource
    Electronic Resource
    Least absolute value and chebychev estimation utilizing least squares results (1982)
    Springer
    Mathematical programming 24 (1982), S. 346-352 
    Details
    ISSN: 1436-4646
    Keywords: Least Absolute Values ; Chebychev Norm ; Regression ; Minimax ; Advanced Start ; Least Squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In exploratory data analysis and curve fitting in particular, it is often desirable to observe residual values obtained with different estimation criteria. The goal with most linear model curve-fitting procedures is to minimize, in some sense, the vector of residuals. Perhaps three of the most common estimation criteria require minimizing: the sum of the absolute residuals (least absolute value or L1 norm); the sum of the squared residuals (least squares or L2 norm); and the maximum residual (Chebychev or L∞ norm). This paper demonstrates that utilizing the least squares residuals to provide an advanced start for the least absolute value and Chebychev procedures results in a significant reduction in computational effort. Computational results are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585115
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  • 4
    Electronic Resource
    Electronic Resource
    Improved penalty calculations for a mixed integer branch-and-bound algorithm (1974)
    Springer
    Mathematical programming 6 (1974), S. 212-223 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents an extension of Tomlin's penalties for the branch-and-bound linear mixed integer programming algorithm of Beale and Small. Penalties which are uniformly stronger are obtained by jointly conditioning on a basic variable and the non-basic variable yielding the Tomlin penalty. It is shown that this penalty can be computed with a little additional arithmetic and some extra bookkeeping. The improvement is easy to incorporate for the normal case as well as when the variables are grouped into ordered sets with generalized upper bounds. Computational experience bears out the usefulness of the extra effort for predominantly integer problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580237
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