A simple effective heuristic for embedded mixed-integer quadratic programming
In this paper, we propose a fast optimisation algorithm for approximately minimising convex quadratic functions over the intersection of affine and separable constraints (i.e. the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-inte...
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| Veröffentlicht in: | International journal of control Jg. 93; H. 1; S. 2 - 12 |
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| Sprache: | Englisch |
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Abingdon
Taylor & Francis
02.01.2020
Taylor & Francis Ltd |
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| ISSN: | 0020-7179, 1366-5820 |
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| Abstract | In this paper, we propose a fast optimisation algorithm for approximately minimising convex quadratic functions over the intersection of affine and separable constraints (i.e. the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimisation problems. We discuss the favourable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value; indeed, we see that in many cases, it finds the global solution. |
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| AbstractList | In this paper, we propose a fast optimisation algorithm for approximately minimising convex quadratic functions over the intersection of affine and separable constraints (i.e. the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimisation problems. We discuss the favourable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value; indeed, we see that in many cases, it finds the global solution. |
| Author | Bemporad, Alberto Takapoui, Reza Boyd, Stephen Moehle, Nicholas |
| Author_xml | – sequence: 1 givenname: Reza surname: Takapoui fullname: Takapoui, Reza email: takapoui@stanford.edu organization: Department of Electrical Engineering, Stanford University – sequence: 2 givenname: Nicholas surname: Moehle fullname: Moehle, Nicholas organization: Mechanical Engineering Department, Stanford University – sequence: 3 givenname: Stephen surname: Boyd fullname: Boyd, Stephen organization: Information Systems Laboratory, Department of Electrical Engineering, Stanford University – sequence: 4 givenname: Alberto surname: Bemporad fullname: Bemporad, Alberto organization: IMT Institute for Advanced Studies Lucca |
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| SubjectTerms | ADMM Algorithms Cartesian coordinates embedded applications Embedded systems heuristic Hybrid electric vehicles Integers Mathematical analysis Mixed-integer quadratic programming Optimization Power converters Powertrain Quadratic equations Quadratic programming |
| Title | A simple effective heuristic for embedded mixed-integer quadratic programming |
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