Friday, 10:30 - 10:55 h, Room: H 2038

 

Mirai Tanaka
Numerical computation of a facial reduction algorithm and an inexact primal-dual path-following method for doubly nonnegative optimization problems

Coauthors: Kazuhide Nakata, Hayato Waki

 

Abstract:
In this talk, we introduce an effective approach to solve
doubly nonnegative relaxation (DNR) problems for mixed binary nonconvex quadratic optimization problems.
In our approach, we convert a given DNR problem into another one that is smaller than the original one exploiting degeneracy.
We can expect numerical stability of interior-point methods for the DNR problem to be improved
because this conversion can be regarded as an incomplete facial reduction algorithm.
In a previous approach, we can find degeneracy only relevant to semidefiniteness analytically.
In our approach, to also find degeneracy relevant to nonnegativity,
we compute a dense optimal solution of a linear optimization problem with an interior-point method.
Moreover, we propose an inexact primal-dual path-following method for the reduced DNR problems.
In our algorithm, to compute search directions,
we solve large linear systems via the preconditioned symmetric quasi-minimal residual (PSQMR) method.
To accelerate the convergence of the PSQMR method,
we develop some preconditioners.
Numerical results show that we can solve some instances of DNR problems quickly and accurately.

 

Talk 1 of the invited session Fri.1.H 2038
"Recent developments of theory and applications in conic optimization II" [...]
Cluster 4
"Conic programming" [...]

 

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