IEICE TRANSACTIONS on Fundamentals
On the Uesaka's Conjecture as to the Optimization by Means of Neural Networks for Combinatorial Problems
Summary :
This paper gives two kinds of functions for which Uesaka's Conjecture, stating that the globally optimum (not a local minimum) of a quadratic function F(x)=-(1/2)xtAx in the n-dimensional hypercube may be obtained by solving a differential equation, holds true, where n denotes the dimension of the vector x. Uesaka stated in his paper that he proved the conjecture only for n=2. This corresponds to a very special case of this paper. The results of this paper suggest that the conjecture really holds for a wide class of quadratic functions and therefore support the conjecture partially.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.9 pp.1811-1817
- Publication Date
- 1998/09/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
- Category
- Neural Networks
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Tetsuo NISHI, "On the Uesaka's Conjecture as to the Optimization by Means of Neural Networks for Combinatorial Problems" in IEICE TRANSACTIONS on Fundamentals,
vol. E81-A, no. 9, pp. 1811-1817, September 1998, doi: .
Abstract: This paper gives two kinds of functions for which Uesaka's Conjecture, stating that the globally optimum (not a local minimum) of a quadratic function F(x)=-(1/2)xtAx in the n-dimensional hypercube may be obtained by solving a differential equation, holds true, where n denotes the dimension of the vector x. Uesaka stated in his paper that he proved the conjecture only for n=2. This corresponds to a very special case of this paper. The results of this paper suggest that the conjecture really holds for a wide class of quadratic functions and therefore support the conjecture partially.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_9_1811/_p
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@ARTICLE{e81-a_9_1811,
author={Tetsuo NISHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Uesaka's Conjecture as to the Optimization by Means of Neural Networks for Combinatorial Problems},
year={1998},
volume={E81-A},
number={9},
pages={1811-1817},
abstract={This paper gives two kinds of functions for which Uesaka's Conjecture, stating that the globally optimum (not a local minimum) of a quadratic function F(x)=-(1/2)xtAx in the n-dimensional hypercube may be obtained by solving a differential equation, holds true, where n denotes the dimension of the vector x. Uesaka stated in his paper that he proved the conjecture only for n=2. This corresponds to a very special case of this paper. The results of this paper suggest that the conjecture really holds for a wide class of quadratic functions and therefore support the conjecture partially.},
keywords={},
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ISSN={},
month={September},}
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TY - JOUR
TI - On the Uesaka's Conjecture as to the Optimization by Means of Neural Networks for Combinatorial Problems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1811
EP - 1817
AU - Tetsuo NISHI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1998
AB - This paper gives two kinds of functions for which Uesaka's Conjecture, stating that the globally optimum (not a local minimum) of a quadratic function F(x)=-(1/2)xtAx in the n-dimensional hypercube may be obtained by solving a differential equation, holds true, where n denotes the dimension of the vector x. Uesaka stated in his paper that he proved the conjecture only for n=2. This corresponds to a very special case of this paper. The results of this paper suggest that the conjecture really holds for a wide class of quadratic functions and therefore support the conjecture partially.
ER -
English
