On the quadratic programming algorithm of Goldfarb and Idnani. Two implementations of the algorithm of D. Goldfarb and A. Idnani [Math. Program. 27, 1-33 (1983; Zbl 0537.90081)] for convex quadratic programming are considered. A pathological example shows that the faster one can be unstable, but numerical testing on some difficult problems indicates that both implementations give excellent accuracy. Therefore the author has provided for general use a Fortran subroutine [”ZQPCVX: a Fortran subroutine for convex, quadratic programming”, Report DAMTP/1983/NA17, Dept. Appl. Math. Theor. Phys., Univ. of Cambridge (1983)] that applies the faster implementation. This subroutine is compared with two widely available quadratic programming subroutines that employ feasible point methods, namely QPSOL [see P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, ”User’s guide for SOL/QPSOL: A Fortran package for quadratic programming”, Report SOL 83-7, Systems Optim. Lab., Rept. Oper. Res., Stanford Univ. (1983)] and VEO2A [see R. Fletcher, ”A Fortran subroutine for general quadratic programming”, Report AERE-R 6370, Harwell (1970)]. We conclude that the algorithm of Goldfarb and Idnani is very suitable in practice for convex quadratic programming calculations.

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  1. Stefanova, Maria; Minevich, Olga; Baklanov, Stanislav; Petukhova, Margarita; Lupuleac, Sergey; Grigor’ev, Boris; Kokkolaras, Michael: Convex optimization techniques in compliant assembly simulation (2020)
  2. Gould, Nicholas I. M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
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  5. Exler, Oliver; Lehmann, Thomas; Schittkowski, Klaus: A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization (2012)
  6. Kirches, Christian; Bock, Hans Georg; Schlöder, Johannes P.; Sager, Sebastian: A factorization with update procedures for a KKT matrix arising in direct optimal control (2011)
  7. Sapountzakis, E. J.; Kampitsis, A. E.: Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation (2011)
  8. Andretta, Marina; Birgin, Ernesto G.; Martínez, J. M.: Partial spectral projected gradient method with active-set strategy for linearly constrained optimization (2010)
  9. Vassiliou, E. E.; Demetriou, I. C.: A linearly distributed lag estimator with (r)-convex coefficients (2010)
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  13. Übi, E.: A numerically stable least squares solution to the quadratic programming problem (2008)
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  19. Fujishige, S.; Liu, Xiaojun; Zhang, X.: An algorithm for solving the minimum-norm point problem over the intersection of a polytope and an affine set (2000)
  20. Frangioni, Antonio: Solving semidefinite quadratic problems within nonsmooth optimization algorithms (1996)

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