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References
Hestenes, C.: Multiplier and gradient methods. J. Optim. Theory Appl. 4, 303–320 (1969)
Powell, M.J.D.: A Method for Nonlinear Constraints in Minimization Problems. Optimization, pp. 283–298. Academic, New York (1969)
Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic, London (1982)
Glowinski, R., Le Tallec, P.: Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia (1989)
Conn, A.R., Gould, N.I.M., Toint, PhL: LANCELOT: A FORTRAN Package for Large Scale Nonlinear Optimization (Release A). Springer Series in Computational Mathematics, vol. 17. Springer, New York (1992)
Hager, W.W.: Analysis and implementation of a dual algorithm for constraint optimization. J. Optim. Theory Appl. 79, 37–71 (1993)
Dostál, Z., Friedlander, A., Santos, S.A.: Augmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraints. SIAM J. Optim. 13, 1120–1140 (2003)
Dostál, Z., Kučera, R.: An optimal algorithm for minimization of quadratic functions with bounded spectrum subject to separable convex inequality and linear equality constraints. SIAM J. Optim. 20(6), 2913–2938 (2010)
Dostál, Z., Kozubek, T.: An optimal algorithm with superrelaxation for minimization of a quadratic function subject to separable constraints with applications. Math. Program. Ser. A 135, 195–220 (2012)
Dostál, Z., Brzobohatý, T., Horák, D., Kozubek, T., Vodstrčil, P.: On R-linear convergence of semi-monotonic inexact augmented Lagrangians for bound and equality constrained quadratic programming problems with application. Comput. Math. Appl. 67(3), 515–526 (2014)
Dostál, Z.: Optimal Quadratic Programming Algorithms, with Applications to Variational Inequalities, 1st edn. Springer, New York (2009)
Conn, A.R., Gould, N.I.M., Toint, Ph.L.: A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28, 545–572 (1991)
Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust Region Methods. SIAM, Philadelphia (2000)
Birgin, E.M., Martínez, J.M.: Practical Augmented Lagrangian Method. SIAM, Philadelphia (2014)
Friedlander, M.P., Leyfer, S.: Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs. SIAM J. Sci. Comput. 30(4), 1706–1729 (2008)
Dostál, Z.: Inexact semi-monotonic augmented Lagrangians with optimal feasibility convergence for quadratic programming with simple bounds and equality constraints. SIAM J. Numer. Anal. 43(1), 96–115 (2005)
Dostál, Z., Horák, D.: Scalable FETI with optimal dual penalty for a variational inequality. Numer. Linear Algebra Appl. 11(5–6), 455–472 (2004)
Dostál, Z., Horák, D.: Scalable FETI with optimal dual penalty for semicoercive variational inequalities. Contemp. Math. 329, 79–88 (2003)
Dostál, Z.: An optimal algorithm for bound and equality constrained quadratic programming problems with bounded spectrum. Computing 78, 311–328 (2006)
Bertsekas, D.P.: Nonlinear Optimization. Athena Scientific, Belmont (1999)
Bouchala, J., Dostál, Z., Kozubek, T., Pospíšil, L., Vodstrčil, P.: On the solution of convex QPQC problems with elliptic and other separable constraints. Appl. Math. Comput. 247(15), 848–864 (2014)
Hapla, V.: Massively parallel quadratic programming solvers with applications in mechanics. Ph.D. Thesis, FEECS, VŠB–Technical University of Ostrava, Ostrava (2016)
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Dostál, Z., Kozubek, T. (2023). Solvers for Separable and Equality QP/QCQP Problems. In: Scalable Algorithms for Contact Problems. Advances in Mechanics and Mathematics, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-33580-8_9
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