A branch-and-cut algorithm for solving mixed-integer semidefinite optimization problems

Ken Kobayashi () and Yuich Takano
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Ken Kobayashi: Fujitsu Laboratories LTD.
Yuich Takano: University of Tsukuba

Computational Optimization and Applications, 2020, vol. 75, issue 2, No 7, 493-513

Abstract: Abstract We consider a cutting-plane algorithm for solving mixed-integer semidefinite optimization (MISDO) problems. In this algorithm, the positive semidefinite (psd) constraint is relaxed, and the resultant mixed-integer linear optimization problem is solved repeatedly, imposing at each iteration a valid inequality for the psd constraint. We prove the convergence properties of the algorithm. Moreover, to speed up the computation, we devise a branch-and-cut algorithm, in which valid inequalities are dynamically added during a branch-and-bound procedure. We test the computational performance of our cutting-plane and branch-and-cut algorithms for three types of MISDO problem: random instances, computing restricted isometry constants, and robust truss topology design. Our experimental results demonstrate that, for many problem instances, our branch-and-cut algorithm delivered superior performance compared with general-purpose MISDO solvers in terms of computational efficiency and stability.

Keywords: Mixed-integer optimization; Semidefinite optimization; Cutting-plane algorithm; Branch-and-cut algorithm (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-019-00153-2

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