Weigandt, Anna; Tuthill, Kaitlyn; Jibrin, Shafiu Constraint consensus methods for finding interior feasible points in second-order cones. (English) Zbl 1208.90188 J. Appl. Math. 2010, Article ID 307209, 19 p. (2010). Summary: Optimization problems with second-order cone constraints (SOCs) can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck’s Original constraint consensus method and DBmax constraint consensus method to find near-feasible points for systems of SOCs. We also develop and implement a new backtracking-like line search technique on these methods that attempts to increase the length of the consensus vector, at each iteration, with the goal of finding interior feasible points. Our numerical results indicate that the new methods are effective in finding interior feasible points for SOCs. Cited in 1 Document MSC: 90C51 Interior-point methods 90C30 Nonlinear programming Keywords:near-feasible point; backtracking-like line search Software:LPbook × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, “Applications of second-order cone programming,” Linear Algebra and Its Applications, vol. 284, no. 1-3, pp. 193-228, 1998. · Zbl 0946.90050 · doi:10.1016/S0024-3795(98)10032-0 [2] F. Alizadeh and D. Goldfarb, “Second-order cone programming,” Mathematical Programming, vol. 95, no. 1, pp. 3-51, 2003. · Zbl 1153.90522 · doi:10.1007/s10107-002-0339-5 [3] J. W. Chinneck, “The constraint consensus method for finding approximately feasible points in nonlinear programs,” Informs Journal on Computing, vol. 16, no. 3, pp. 255-265, 2004. · Zbl 1239.90096 [4] Y. Nesterov and A. Nemirovsky, “Interior-Point polynomial methods in convex programming,” in Studies in Applied Mathematics, vol. 13, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0824.90112 [5] R. J. Caron, T. Traynor, and S. Jibrin, “Feasibility and constraint analysis of sets of linear matrix inequalities,” Informs Journal on Computing, vol. 22, no. 1, pp. 144-153, 2010. · Zbl 1243.90172 [6] J. W. Chinneck, Private communication with S. Jibrin, 2010. [7] D. den Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming, vol. 277 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994. · Zbl 0808.90107 [8] R. J. Vanderbei, Linear Programming: Foundations and Extensions, Kluwer Academic Publishers, Boston, Mass, USA, Second edition, 2001. · Zbl 1043.90002 [9] W. Ibrahim and J. W. Chinneck, “Improving solver success in reaching feasibility for sets of nonlinear constraints,” Computers & Operations Research, vol. 35, no. 5, pp. 1394-1411, 2008. · Zbl 1278.90381 · doi:10.1016/j.cor.2006.08.002 [10] Y. Censor and S. A. Zenios, Parallel Optimization: Theory, Algorithms, and Applications, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, NY, USA, 1997. · Zbl 0945.90064 [11] D. Butnariu, Y. Censor, and S. Reich, Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, vol. 8 of Studies in Computational Mathematics, North-Holland Publishing, Amsterdam, The Netherlands, 2001. · Zbl 0971.00058 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.