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896. Lagrangian duality for Mixed-Integer Semidefinite Programming
Invited abstract in session WB-38: Convex and conic optimization, stream Conic Optimization: Theory, Algorithms, and Applications.
Wednesday, 10:30-12:00Room: 34 (building: 306)
Authors (first author is the speaker)
| 1. | Renata Sotirov
|
| Tilburg University | |
| 2. | Frank de Meijer
|
| Delft Institute of Applied Mathematics, Delft University of Technology |
Abstract
Mixed-integer semidefinite programming can be viewed as a generalization of mixed-integer programming where the vector of variables is replaced by mixed-integer positive semidefinite matrix variables. The combination of positive semidefiniteness and integrality allows to formulate various nonlinear optimization problems as mixed-integer semidefinite programs (MISDPs).
In this talk we show that MISDPs induce bounds based on Lagrangian duality theory. By introducing MISDP-based projected bundle algorithm, we show that the resulting Lagrangian dual bounds are stronger than the standard SDP bounds for various optimization problems.
Keywords
- Convex Optimization
- Mathematical Programming
- Combinatorial Optimization
Status: accepted
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