Monday, 15:45 - 16:10 h, Room: H 2053

 

Takahito Kuno
A class of convergent subdivision strategies in the conical algorithm for concave minimization

Coauthor: Tomohiro Ishihama

 

Abstract:
We present a new proof of the convergence of the conical algorithm for concave minimization under a pure ω-subdivision strategy.
In 1991, Tuy showed that the conical algorithm with ω-subdivision is convergent if a certain kind of nondegeneracy holds for sequences of nested cones generated in the process of the algorithm.
Although the convergence has already been proven in other ways, it still remains an open question whether the sequences are nondegenerate or not.
In this talk, we introduce a weaker condition of nondegeneracy,
named pseudo-nondegeneracy, and show that the conical algorithm
with ω-subdivision converges as long as the pseudo-nondegeneracy holds for sequences of nested cones generated by the algorithm.
We also show that every sequence generated by the algorithm is pseudo-nondegenerate.
The pseudo-nondegeneracy is not only a useful condition for proving the convergence, but suggests a possible class of convergent subdivision strategies.

 

Talk 2 of the invited session Mon.3.H 2053
"Algorithms and relaxations for nonconvex optimization Problems" [...]
Cluster 9
"Global optimization" [...]

 

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