Characterizations of minimal elements of topical functions on semimodules with applications
- Authors: Hassani, Sara , Mohebi, Hossein
- Date: 2017
- Type: Text , Journal article
- Relation: Linear Algebra and Its Applications Vol. 520, no. (2017), p. 104-124
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- Description: In this paper, we first give characterizations of the superdifferential of extended valued topical functions defined on a semimodule with values in a semifield. Next, we characterize minimal elements of the upper support set of extended valued topical functions. Finally, as an application, we present a necessary and sufficient condition for global maximum of the difference of two strictly topical functions defined on a semimodule. (C) 2017 Elsevier Inc. All rights reserved.
Global optimal solutions to general sensor network localization problem
- Authors: Ruan, Ning , Gao, David
- Date: 2014
- Type: Text , Journal article
- Relation: Performance Evaluation Vol. 75-76, no. (2014), p. 1-16
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- Description: Sensor network localization problem is to determine the position of the sensor nodes in a network given pairwise distance measurements. Such problem can be formulated as a quartic polynomial minimization via the least squares method. This paper presents a canonical duality theory for solving this challenging problem. It is shown that the nonconvex minimization problem can be reformulated as a concave maximization dual problem over a convex set in a symmetrical matrix space, and hence can be solved efficiently by combining a general (linear or quadratic) perturbation technique with existing optimization techniques. Applications are illustrated by solving some relatively large-scale problems. Our results show that the general sensor network localization problem is not NP-hard unless its canonical dual problem has no solution in its positive definite domain. Fundamental ideas for solving general NP-hard problems are discussed. (C) 2014 Elsevier B.V. All rights reserved.
Stable trajectory of logistic map
- Authors: Li, Chaojie , Zhou, Xiaojun , Gao, David
- Date: 2014
- Type: Text , Journal article
- Relation: Nonlinear Dynamics Vol. 78, no. 1 (2014), p. 209-217
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- Description: In this paper, the stable trajectory of Logistic Map has been investigated by canonical duality theory from the perspective of global optimization. Numerical result of our method shows that it totally differs from traditional chaotic solution solved by Euler method. In addition, we have applied our method to three well-known standard benchmarks in global optimization. Numerical simulations are given to illustrate the effectiveness of the main results.