Duality for mixed-integer convex minimization
We extend in two ways the standard Karush–Kuhn–Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard Karush–Kuhn–Tucker conditions involve separating hyperplanes, our...
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| Veröffentlicht in: | Mathematical programming 2016-07, Vol.158 (1-2), p.547-564 |
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| container_title | Mathematical programming |
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| creator | Baes, Michel Oertel, Timm Weismantel, Robert |
| description | We extend in two ways the standard Karush–Kuhn–Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard Karush–Kuhn–Tucker conditions involve separating hyperplanes, our extension is based on mixed-integer-free polyhedra. Our optimality conditions allow us to define an exact dual of our original mixed-integer convex problem. |
| doi_str_mv | 10.1007/s10107-015-0917-y |
| format | Article |
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| subjects | Calculus of Variations and Optimal Control Optimization Combinatorics Convex analysis Integer programming Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operations research Optimization Short Communication Studies Theoretical |
| title | Duality for mixed-integer convex minimization |
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