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  • 1
    Electronic Resource
    Electronic Resource
    Optimization over the efficient set: Four special cases (1994)
    Springer
    Journal of optimization theory and applications 80 (1994), S. 3-18 
    Details
    ISSN: 1573-2878
    Keywords: Multiple criteria decision making ; efficient set ; global optimization ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, researchers and practitioners have been increasingly interested in the problem (P) of maximizing a linear function over the efficient set of a multiple objective linear program. Problem (P) is generally a difficult global optimization problem which requires numerically intensive procedures for its solution. In this paper, simple linear programming procedures are described for detecting and solving four special cases of problem (P). When solving instances of problem (P), these procedures can be used as screening devices to detect and solve these four special cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02196590
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem (1996)
    Springer
    Journal of optimization theory and applications 88 (1996), S. 77-105 
    Details
    ISSN: 1573-2878
    Keywords: Multiple criteria decision making ; efficient set ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article presents a finite, outcome-based algorithm for optimizing a lower semicontinuous function over the efficient set of a bicriteria linear programming problem. The algorithm searches the efficient faces of the outcome set of the bicriteria linear programming problem. It exploits the fact that the dimension of the outcome set of the bicriteria problem is at most two. As a result, in comparison to decisionbased approaches, the number of efficient faces that need to be found is markedly reduced. Furthermore, the dimensions of the efficient faces found are always at most one. The algorithm can be implemented for a wide variety of lower semicontinuous objective functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192023
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    Paper (German National Licenses)
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