On the computational complexity of membership problems for the completely positive cone and its dual

Berman, A., Shaked-Monderer, N.: Completely Positive Matrices. World Scientific, Singapore (2003)

Bomze, I.M.: Copositive programming—recent developments and applications. Cent. Eur. J. Oper. Res. 216, 509–520 (2012)

Bomze, I.M., Jarre, F., Rendl, F.: Quadratic factorization heuristics for copositive programming. Math. Program. Comput. 3(1), 37–57 (2011)

Bomze, I.M., Schachinger, W., Uchida, G.: Think co(mpletely) positive! matrix properties, examples and a clustered bibliography on copositive optimization. J. Glob. Optim. 52(3), 423–445 (2012)

Bondy, J., Murty, U.: Graph Theory with Applications. Macmillan, London (1976)

Bundfuss, S., Dür, M.: An adaptive linear approximation algorithm for copositive programs. SIAM J. Optim. 20(1), 30–53 (2009)

Burer, S.: Copositive programming. In: Handbook of Semidefinite, Cone and Polynomial Optimization: Theory, Algorithms, Software and Applications, pp. 201–218. Springer, New York (2012)

Burer, S.: On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Program. 120(2), 479–495 (2009)

de Klerk, E.: The complexity of optimizing over a simplex, hypercube or sphere: a short survey. Cent. Eur. J. Oper. Res. 16(2), 111–125 (2008)

de Klerk, E., Pasechnik, D.: Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12(4), 875–892 (2002)

Dickinson, P.J.C.: The copositive cone, the completely positive cone and their generalisations. Ph.D. thesis, University of Groningen (2013)

Dickinson, P.J.C., Dür, M.: Linear-time complete positivity detection and decomposition of sparse matrices. SIAM J. Matrix Anal. Appl. 33(3), 701–720 (2012)

Dür, M.: Copositive programming—a survey. In: Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds.) Recent Advances in Optimization and Its Applications in Engineering, pp. 3–20. Springer, Berlin (2010)

Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin (1988)

Gvozdenović, N., Laurent, M.: The operator Ψ for the chromatic number of a graph. SIAM J. Optim. 19(2), 572–591 (2008)

Hiriart-Urruty, J.B., Seeger, A.: A variational approach to copositive matrices. SIAM Rev. 52(4), 593–629 (2010)

Jarre, F., Schmallowsky, K.: On the computation of certificates. J. Glob. Optim. 45(2), 281–296 (2009)

Kaykobad, M.: On nonnegative factorization of matrices. Linear Algebra Appl. 96, 27–33 (1987)

Murty, K., Kabadi, S.: Some NP-complete problems in quadratic and nonlinear programming. Math. Program. 39(2), 117–129 (1987)

Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Algorithms and Combinatorics, vol. 24. Springer, Berlin (2003)

Yudin, D., Nemirovskii, A.: Informational complexity and efficient methods for the solution of convex extremal problems. Èkon. Mat. Metody 12(2), 357–369 (1976). English translation: Matekon 13(3) (1977) 25–45