Abstract
This paper presents a canonical dual approach for solving a general nonconvex problem in network optimization. Three challenging problems, sensor network location, traveling salesman problem, and scheduling problem are listed to illustrate the applications of the proposed method. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques.
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References
Gao, D.Y.: Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Kluwer Academic Publishers, Dordrecht (2000)
Gao, D.Y., Ruan, N.: Solutions to Quadratic Minimization Problems with Box and Integer Constraints. J. Global Optim. 47, 463–484 (2010)
Gao, D.Y., Ruan, N., Pardalos, P.M.: Canonical Dual Solutions to Sum of Fourth-Order Polynomials Minimization Problems with Applications to Sensor Network Localization. In: Boginski, V.L., Commonder, C.W., Pardalos, P.M., Ye, Y.Y. (eds.) Sensors: Theory, Algorithms and Applications, vol. 61, pp. 37–54. Springer (2012)
Gao, D.Y., Ruan, N., Sherali, H.D.: Solutions and Optimality Criteria for Nonconvex Constrained Global Optimization Problems. J. Global Optim. 45, 473–497 (2009)
Gao, D.Y., Watson, L.T., Easterling, D.R., Thacker, W.I., Billups, S.C.: Solving the Canonical Dual of Box- and Integer-Constrained Nonconvex Quadratic Programs via a Deterministic Direct Search Algorithm. Optim. Method Softw. (2011), doi:10.1080/10556788.2011.641125
Gao, D.Y., Wu, C.Z.: On the Triality Theory for a Quartic Polynomial Optimization Problem. J. Ind. Manag. Optim. 8, 229–242 (2012)
Ruan, N., Gao, D.C., Jiao, Y.: Canonical Dual Least Square Method for Solving General Nonlinear Systems of Equations. Comput. Optim. Appl. 47, 335–347 (2010)
Smith, K.: An Argument for Abandoning the Traveling Salesman Problem as a Neural-Network Benchmark. IEEE Trans. Neural Networks 7, 1542–1544 (1996)
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Ruan, N., Yang Gao, D. (2012). Canonical Duality Theory and Algorithm for Solving Challenging Problems in Network Optimisation. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34487-9_85
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DOI: https://doi.org/10.1007/978-3-642-34487-9_85
Publisher Name: Springer, Berlin, Heidelberg
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