Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm
In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems,...
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| Published in: | Computational optimization and applications Vol. 34; no. 1; pp. 63 - 83 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York
Springer Nature B.V
01.05.2006
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems. |
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| AbstractList | In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems. In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems. [PUBLICATION ABSTRACT] |
| Author | Still, Claus Westerlund, Tapio |
| Author_xml | – sequence: 1 givenname: Claus surname: Still fullname: Still, Claus – sequence: 2 givenname: Tapio surname: Westerlund fullname: Westerlund, Tapio |
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| CitedBy_id | crossref_primary_10_1016_j_cep_2022_109263 crossref_primary_10_1007_s10898_014_0217_8 crossref_primary_10_1016_j_ejor_2009_01_033 crossref_primary_10_1108_03684920910973180 crossref_primary_10_1155_2017_8763101 crossref_primary_10_1007_s12532_020_00196_1 crossref_primary_10_1007_s10479_018_2872_5 crossref_primary_10_1007_s12532_021_00212_y crossref_primary_10_1017_S0962492913000032 crossref_primary_10_1108_03684920710749730 crossref_primary_10_1007_s11081_020_09536_5 crossref_primary_10_1109_TPWRS_2017_2727323 crossref_primary_10_1109_TSG_2016_2542180 crossref_primary_10_1007_s00158_015_1225_0 crossref_primary_10_1002_nav_20432 |
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| SubjectTerms | Algorithms Approximation Capital budgeting Linear programming Mathematical models Optimization Studies |
| Title | Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm |
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