A Continuous-Time Distributed Algorithm for Solving a Class of Decomposable Nonconvex Quadratic Programming

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Abstract

In this paper, a continuous-time distributed algorithm is presented to solve a class of decomposable quadratic programming problems. In the quadratic programming, even if the objective function is nonconvex, the algorithm can still perform well under an extra condition combining with the objective, constraint and coupling matrices. Inspired by recent advances in distributed optimization, the proposed continuous-time algorithm described by multi-agent network with consensus is designed and analyzed. In the network, each agent only accesses the local information of its own and from its neighbors, then all the agents in a connected network cooperatively find the optimal solution with consensus.

[1] R. H. Byrd, M. E. Hribar, and J. Nocedal, An interior point algorithm for large-scale nonlinear programming, SIAM Journal on Optimization, vol. 9, no. 4, pp. 877-900, 1999.

[2] M. A. Figueiredo, R. D. Nowak, and S. J. Wright, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems, IEEE Journal of Selected Topics in Signal Processing, vol. 1, no. 4, pp. 586-597, Dec. 2007.

[3] J. Hopfield and D. Tank, Computing with neural circuits: A model, Science, vol. 233, no. 4764, pp. 625-633, 1986.

[4] Y. Xia, G. Feng, and J. Wang, A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints, IEEE Transactions on Neural Networks, vol. 19, no. 8, pp. 1340-1353, Aug. 2008.

[5] Q. Liu and J. Wang, L1-minimization algorithms for sparse signal reconstruction based on a projection neural network, IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 3, pp. 698-707, Mar. 2016.

[6] Q. Liu and J. Wang, A projection neural network for constrained quadratic minimax optimization, IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 11, pp. 2891-2900, Nov. 2015.

[7] G. Tambouratzis, Using particle swarm optimization to accurately identify syntactic phrases in free text, Journal of Artificial Intelligence & Soft Computing Research, vol. 8, no. 1, pp. 63-67, 2018.

[8] S. Sadiqbatcha, J. Saeed, and A. Yiannis, Particle swarm optimization for solving a class of type-1 and type-2 fuzzy nonlinear equations, Journal of Artificial Intelligence & Soft Computing Research, vol. 8, no. 2, pp. 103-110, 2018.

[9] C. Rotar and L. B. Iantovics, Directed evolution - a new metaheuristc for optimization, Journal of Artificial Intelligence & Soft Computing Research, vol. 7, no. 3, pp. 183-200, 2017.

[10] J. Antonio, G. Huang, and W. Tsai, A fast distributed shortest path algorithm for a class of hierarchically clustered data networks, IEEE Transactions on Computers, pp. 710-724, 1992.

[11] S. Sundhar Ram, A. Nedić, and V. V. Veeravalli, A new class of distributed optimization algorithms: Application to regression of distributed data, Optimization Methods and Software, vol. 27, no. 1, pp. 71-88, 2012.

[12] L. Xiao, S. Boyd, and S.-J. Kim, Distributed average consensus with least-mean-square deviation, Journal of Parallel and Distributed Computing, vol. 67, no. 1, pp. 33-46, 2007.

[13] A. Nedic, A. Ozdaglar, and P. A. Parrilo, Constrained consensus and optimization in multi-agent networks, IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 922-938, Apr. 2010.

[14] M. Zhu and S. Martínez, On distributed convex optimization under inequality and equality constraints, IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 151-164, Jan. 2012.

[15] D. Yuan, S. Xu, and H. Zhao, Distributed primaldual subgradient method for multiagent optimization via consensus algorithms, IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics, vol. 41, no. 6, pp. 1715-1724, Dec. 2011.

[16] B. Gharesifard and J. Cortés, Distributed continuous-time convex optimization on weightbalanced digraphs, IEEE Transactions on Automatic Control, vol. 59, no. 3, pp. 781-786, Mar. 2014.

[17] Q. Liu and J. Wang, A second-order multi-agent network for bound-constrained distributed optimization, IEEE Transactions on Automatic Control, vol. 60, no. 12, pp. 3310-3315, Dec. 2015.

[18] M. Rabbat and R. Nowak, Distributed optimization in sensor networks, in Proc. 3rd International Symposium on Information Processing in Sensor Networks, Berkeley, CA, USA, Apr. 2004, pp. 20-27.

[19] J. F. Mota, J. M. Xavier, P. M. Aguiar, and M. Püschel, Distributed optimization with local domains: Applications in MPC and network flows, IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 2004-2009, July 2015.

[20] W. Ren and R. W. Beard, Distributed Consensus in Multi-vehicle Cooperative Control. Springer- Verlag London Limited, 2008.

[21] A. Nedić and A. Ozdaglar, Subgradient methods for saddle-point problems, Journal of optimization theory and applications, vol. 142, no. 1, pp. 205- 228, 2009.

[22] I. Lobel, A. Ozdaglar, and D. Feijer, Distributed multi-agent optimization with state-dependent communication, Mathematical Programming, vol. 129, no. 2, pp. 255-284, 2011.

[23] P. Lin, W. Ren, and Y. Song, Distributed multiagent optimization subject to nonidentical constraints and communication delays, Automatica, vol. 65, pp. 120-131, 2016.

[24] M. Bürger, G. Notarstefano, and F. Allgöwer, A polyhedral approximation framework for convex and robust distributed optimization, IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 384-395, Feb. 2014.

[25] L. Carlone, V. Srivastava, F. Bullo, and G. C. Calafiore, Distributed random convex programming via constraints consensus, SIAM Journal on Control and Optimization, vol. 52, no. 1, pp. 629- 662, 2014.

[26] X.Wang, Y. Hong, and H. Ji, Distributed optimization for a class of nonlinear multiagent systems with disturbance rejection, IEEE Transactions on Cybernetics, vol. 46, no. 7, pp. 1655-1666, July 2016.

[27] S. Yang, Q. Liu, and J.Wang, Distributed optimization based on a multiagent system in the presence of communication delays, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 5, pp. 717-728, May 2017.

[28] H. Wang, X. Liao, T. Huang, and C. Li, Cooperative distributed optimization in multiagent networks with delays, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 45, no. 2, pp. 363-369, Feb. 2015.

[29] Q. Liu, S. Yang, and J. Wang, A collective neurodynamic approach to distributed constrained optimization, IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 8, pp. 1747- 1758, Aug. 2017.

[30] M. Bazaraa, H. Sherali, and C. Shetty, Nonlinear Programming: Theory and Algorithms (3rd Ed.) Hoboken, New Jersey: John Wiley & Sons, 2006.

[31] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, New York: Academic, 1982.

[32] Q. Liu and K. Li, A continuous-time algorithm based on multi-agent system for distributed least absolute deviation subject to hybrid constraints,” in Proc. 43rd Annual Conference of the IEEE Industrial Electronics Society, 2017, pp. 7381-7386.

[33] J. LaSalle, The Stability of Dynamical Systems Philadelphia, PA, USA: SIAM, 1976.

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

Journal Information

CiteScore 2017: 5.00

SCImago Journal Rank (SJR) 2017: 0.492
Source Normalized Impact per Paper (SNIP) 2017: 2.813

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