An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem

This article presents for the first time an algorithm specifically designed for globally minimizing a finite, convex function over the weakly efficient set of a multiple objective nonlinear programming problem (V1) that has both nonlinear objective functions and a convex, nonpolyhedral feasible regi...

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Bibliographic Details
Published in:Journal of global optimization Vol. 52; no. 3; pp. 553 - 574
Main Author: Benson, Harold P.
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2012
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computer Science
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations management
Operations Research/Decision Theory
Optimization
Pareto optimum
Real Functions
Studies
Global optimization
Multiple objective nonlinear programming
Branch and bound
Weakly efficient set
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:This article presents for the first time an algorithm specifically designed for globally minimizing a finite, convex function over the weakly efficient set of a multiple objective nonlinear programming problem (V1) that has both nonlinear objective functions and a convex, nonpolyhedral feasible region. The algorithm uses a branch and bound search in the outcome space of problem (V1), rather than in the decision space of the problem, to find a global optimal solution. Since the dimension of the outcome space is usually much smaller than the dimension of the decision space, often by one or more orders of magnitude, this approach can be expected to considerably shorten the search. In addition, the algorithm can be easily modified to obtain an approximate global optimal weakly efficient solution after a finite number of iterations. Furthermore, all of the subproblems that the algorithm must solve can be easily solved, since they are all convex programming problems. The key, and sometimes quite interesting, convergence properties of the algorithm are proven, and an example problem is solved.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9786-y