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Numerical Algorithms
Published in: Numerical Algorithms 1/2020

06-11-2019 | Original Paper

Double descent and intermittent color diffusion for landscape exploration

Authors: Luca Dieci, Manuela Manetta, Haomin Zhou

Published in: Numerical Algorithms | Issue 1/2020

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Abstract

In this work, we present a method to explore the landscape of a smooth potential in the search of global minimizers, combining a double-descent technique and a basin-escaping technique based on intermittent colored diffusion. Numerical results illustrate the performance of the method.
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Footnotes
1
As an example, consider the function g1(x, y) = (x2y − x − 1)2 + (x2 − 1)2: it has two local minima at (1,2) and (− 1, 0), and no other critical point.
 
2
Recall \(g:{\mathbb {R}}^{n}\rightarrow {\mathbb {R}}\)is coercive if \(\lim _{\|x\|\rightarrow \infty } g(x)= +\infty \), that is, for any constant M, there is a constant RM such that ∥g(x)∥ > M whenever ∥x∥ > RM.
 
3
The same point can thus appear multiple times in the table.
 
Literature
1.
Aluffi-Pentini, F., Parisi, V., Zirilli, F.: Global optimization and stochastic differential equations. J. Optim. Theo. App. 47 (1986)
2.
Aluffi-Pentini, F., Parisi, V., Zirilli, F.: A global optimization algorithm using stochastic differential equations. ACM Trans. Math. Softw. 14, 345–365 (1988)MathSciNetMATH
3.
4.
Bertsimas, D., Tsitsiklis, J.: Simulated Annealing. Stat. Sci. 8(1), 10–15 (1993)MATH
5.
Chow, S.N., Yang, T.S., Zhou, H.M.: Global optimizations by intermittent diffusion, Chaos, CNN, Memristors and Beyond: a Festschrift for Leon Chua. In: Adamatzky et al. (eds.) . World Scientific Publishing Co. Ltd. (2013)
6.
7.
Dennis, J.E., Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equations. SIAM Classics in Applied Mathematics 16 (1996)
8.
Doye, J.P.K., Leary, R.H., Locatelli, M., Schoen, F.: Global optimization of Morse clusters by potential energy transformations. INFORMS J. Comput. 16(4), 371–379 (2004)MATH
9.
Dixon, L., Szegö, G.P.: Towards Global Optimization. American Elsevier Pub. Co., North Holland (1975)MATH
10.
Dixon, L., Szegö, G.P.: Towards Global Optimization. Elsevier Science Publishing Co Inc., North Holland (1978)
11.
Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, London (1982)MATH
12.
Holmström, K.: New optimization algorithms and software. Theory of Stochastic Processes 5(21), 55–63 (1999)MATH
13.
Jabri, Y.: The Mountain Pass Theorem: Variants, Generalizations and Some Applications. Cambridge University Press, Cambridge (2003)MATH
14.
Kelley, T.: Iterative Methods for Linear and Nonlinear Equations. SIAM Publications, Philadelphia (1995)MATH
15.
Wales, D.J., Doye, J.P.K.: Global optimization by Basin-Hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111 (1997)
16.
Locatelli, M., Shoen, F.: Global Optimization. Theory, Algorithms, and Applications. SIAM-MOS, Philadelphia (2013)
17.
Lourenco, H.R., Matin, O.C., Stütze, T.: Iterated local search. In: Glover, F.W., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp 321–353. Kluwer Academic Publishers, Boston
18.
Mladenovic, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–110 (1997)MathSciNetMATH
19.
Moré, J.J., Munson, T.S.: Computing Mountain Passes, Preprint ANL/MCS-P957-0502, Argonne National Laboratory (2002)
20.
Zhang, J., Du, Q.: Shrinking dimer dynamics and its applications to saddle point search. SIAM J. Numer. Anal. 50-4, 1899–1921 (2012)MathSciNetMATH
Metadata
Title
Double descent and intermittent color diffusion for landscape exploration
Authors
Luca Dieci
Manuela Manetta
Haomin Zhou
Publication date
06-11-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 1/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00807-6

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