A General Regularized Continuous Formulation for the Maximum Clique Problem

References

• [1] Bertsekas DP (1999) Nonlinear Programming (Athena Scientific, Belmont, MA).Google Scholar
• [2] Bomze IM (1997) Evolution towards the maximum clique. J. Global Optim. 10(2):143–164.Crossref, Google Scholar
• [3] Bomze IM (2016) Copositivity for second-order optimality conditions in general smooth optimization problems. Optimization 65(4):779–795.Crossref, Google Scholar
• [4] Bomze IM, Pelillo M, Stix V (2000) Approximating the maximum weight clique using replicator dynamics. IEEE Trans. Neural Network 11(6):1228–1241.Crossref, Google Scholar
• [5] Bomze IM, Budinich M, Pardalos PM, Pelillo M (1999) The Maximum Clique Problem (Springer, Boston), 1–74Crossref, Google Scholar
• [6] Bomze IM, Budinich M, Pelillo M, Rossi C (2002) Annealed replication: A new heuristic for the maximum clique problem. Discrete Appl. Math. 121(13):27–49.Crossref, Google Scholar
• [7] Bradley P, Mangasarian O, Rosen J (1998) Parsimonious least norm approximation. Comput. Optim. Appl. 11(1):5–21.Crossref, Google Scholar
• [8] Frank M, Wolfe P (1956) An algorithm for quadratic programming. Naval Res. Logist. Quart. 3(1/2):95–110.Crossref, Google Scholar
• [9] Gibbons LE, Hearn DW, Pardalos PM (1993) A continuous based heuristic for the maximum clique problem. Johnson DS, Trick M, eds. Second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26 (American Mathematical Society, Providence, RI), 103–124.Google Scholar
• [10] Gibbons LE, Hearn DW, Pardalos PM, Ramana MV (1997) Continuous characterizations of the maximum clique problem. Math. Oper. Res. 22(3):754–768.Link, Google Scholar
• [11] Hager WW, Hungerford JT (2014) Optimality conditions for maximizing a function over a polyhedron. Math. Programming 145(1/2):179–198.Crossref, Google Scholar
• [12] Johnson DS, Trick MA (1996) Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, October 11–13, 1993, vol. 26 (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• [13] Karp R (1972) Reducibility among combinatorial problems. Miller RE, Thatcher JW, eds. Complexity of Computer Computations: Proc. Sympos. Complexity Comput. Comput. (Plenum Press, New York), 85–103.Crossref, Google Scholar
• [14] Keller OH (1930) Über die lückenlose Erfüllung des Raumes mit Würfeln. J. Die Reine Angew Math. 1930(163):231–248.Crossref, Google Scholar
• [15] Kuznetsova A, Strekalovsky A (2001) On solving the maximum clique problem. J. Global Optim. 21(3):265–288.Crossref, Google Scholar
• [16] Motzkin TS, Straus EG (1965) Maxima for graphs and a new proof of a theorem of Turán. Canadian J. Math. 17:533–540.Crossref, Google Scholar
• [17] Murty KG, Kabadi SN (1987) Some NP-complete problems in quadratic and linear programming. Math. Programming 39(2):117–129.Crossref, Google Scholar
• [18] Nocedal J, Wright SJ (2006) Numerical Optimization, 2nd ed. (Springer, New York).Google Scholar
• [19] Pardalos PM, Phillips AT (1990) A global optimization approach for solving the maximum clique problem. Internat. J. Comput. Math. 33(3-4):209–216.Crossref, Google Scholar
• [20] Pardalos PM, Schnitger G (1988) Checking local optimality in constrained quadratic programming can be NP-hard. Oper. Res. Lett. 7(1):33–35.Crossref, Google Scholar
• [21] Pelillo M (1996) Relaxation labeling networks for the maximum clique problem. J. Artificial Neural Networks 2(4):313–328.Google Scholar
• [22] Pelillo M, Jagota A (1996) Feasible and infeasible maxima in a quadratic program for maximum clique. J. Artificial Neural Networks 2(4):411–420.Google Scholar
• [23] Rota-Bulò S, Pelillo M (2009) A generalization of the Motzkin-Straus theorem to hypergraphs. Optim. Lett. 3(2):287–295.Crossref, Google Scholar
• [24] Wu Q, Hao JK (2015) A review on algorithms for maximum clique problems. Eur. J. Oper. Res. 242(3):693–709.Crossref, Google Scholar