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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| Published in: | Journal of global optimization Vol. 52; no. 3; pp. 553 - 574 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
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Boston
Springer US
01.03.2012
Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | 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. |
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| AbstractList | 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.[PUBLICATION ABSTRACT] 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. |
| Author | Benson, Harold P. |
| Author_xml | – sequence: 1 givenname: Harold P. surname: Benson fullname: Benson, Harold P. email: harold.benson@warrington.ufl.edu organization: Department of Information Systems and Operations Management, University of Florida |
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| Keywords | Global optimization Multiple objective nonlinear programming Branch and bound Weakly efficient set |
| Language | English |
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| PublicationSubtitle | An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering |
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| SubjectTerms | Algorithms Approximation Computer Science Mathematics Mathematics and Statistics Nonlinear programming Operations management Operations Research/Decision Theory Optimization Pareto optimum Real Functions Studies |
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| Title | An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem |
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