Open Access
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
Page(s) 2941 - 2950
Published online 13 November 2023
  • R. Andreani, E.G. Birgin, J.M. Martínez and M.L. Schuverdt, On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optim. 18 (2008) 1286–1309. [CrossRef] [Google Scholar]
  • P. Armand and R. Omheni, A mixed logarithmic barrier-augmented lagrangian method for nonlinear optimization. J. Optim. Theory Appl. 173 (2017) 523–547. [CrossRef] [MathSciNet] [Google Scholar]
  • D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. New York, Academic Press (1982). [Google Scholar]
  • E.G. Birgin and J.M. Martínez, Practical Augmented Lagrangian Methods for Constrained Optimization. Vol. 10. SIAM, Philadelphia (2014). [CrossRef] [Google Scholar]
  • E.G. Birgin, R.A. Castillo and J.M. Martínez, Numerical comparison of augmented Lagrangian algorithms for nonconvex problems. Comput. Optim. Appl. 31 (2005) 31–55. [CrossRef] [MathSciNet] [Google Scholar]
  • E.G. Birgin, D. Fernández and J.M. Martínez, The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems. Optim. Methods Softw. 27 (2012) 1001–1024. [CrossRef] [MathSciNet] [Google Scholar]
  • M.G. Breitfeld and D.F. Shanno, Computational experience with penalty-barrier methods for nonlinear programming. Ann. Oper. Res. 62 (1996) 439–463. [CrossRef] [MathSciNet] [Google Scholar]
  • R.H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained Optimization. SIAM J. Sci. Comput. 16 (1995) 1190–1208. [CrossRef] [MathSciNet] [Google Scholar]
  • A.R. Conn, N. Gould and PhL. Toint, A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds. Math. Comput. 66 (1997) 261–288. [CrossRef] [Google Scholar]
  • G. Di Pillo and S. Lucidi, An augmented Lagrangian function with improved exactness properties. SIAM J. Optim. 12 (2001) 376–406. [Google Scholar]
  • N. Echebest, M.D. Sánchez and M.L. Schuverdt, Convergence results of an augmented Lagrangian method using the exponential penalty function. J. Optim. Theory Appl. 168 (2016) 92–108. [CrossRef] [MathSciNet] [Google Scholar]
  • D. Fernández and M.V. Solodov, Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition. SIAM J. Optim. 22 (2012) 384–407. [CrossRef] [MathSciNet] [Google Scholar]
  • M.R. Hestenes, Multiplier and gradient methods. J. Optim. Theory Appl. 4 (1969) 303–320. [CrossRef] [MathSciNet] [Google Scholar]
  • W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems 187, Springer-Verlag, Berlin, Germany (1981). [CrossRef] [Google Scholar]
  • C. Kanzow and D. Steck, An example comparing the standard and safeguarded augmented Lagrangian methods. Oper. Res. Lett. 45 (2017) 598–603. [CrossRef] [MathSciNet] [Google Scholar]
  • B.W. Kort and D.P. Bertsekas, Combined primal-dual and penalty methods for convex programming. SIAM J. Control Optim. 14 (1976) 268–294. [CrossRef] [MathSciNet] [Google Scholar]
  • M.-R. Lennin, The hyperbolic augmented Lagrangian algorithm, Ph.D thesis, Federal University of Rio de Janeiro/COPPE, Rio de Janeiro, Brazil (2022). [Google Scholar]
  • X.W. Liu, Y.H. Dai and Y.K. Sun, A novel augmented lagrangian method of multipliers for optimization with general inequality constraints. Math. Comput. 92 (2023). [Google Scholar]
  • V.H. Nguyen and J.J. Strodiot, On the convergence rate for a penalty function method of exponential type. J. Optim. Theory Appl. 27 (1979) 495–508. [CrossRef] [MathSciNet] [Google Scholar]
  • R. Polyak and M. Teboulle, Nonlinear rescaling and proximal-like methods in convex optimization. Math. Program. 76 (1997) 265–284. [Google Scholar]
  • M.J.D. Powell, A method for nonlinear constraints in minimization problems, edited by R. Fletcher, In: Optimization. Academic Press, New York (1969) 283–298. [Google Scholar]
  • R.T. Rockafellar, Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control. 12 (1974) 268–285. [CrossRef] [MathSciNet] [Google Scholar]
  • P. Tseng and D.P. Bertsekas, On the convergence of the exponential multiplier method for convex programming. Math. Program. 60 (1993) 1–19. [CrossRef] [Google Scholar]
  • C.Y. Wang and D. Li, Unified theory of augmented Lagrangian methods for constrained global optimization. J. Glob. Optim. 44 (2009) 433–458. [CrossRef] [Google Scholar]
  • A.E. Xavier, Penalização Hiperbólica: Um Novo Método para Resolução de Problemas de Otimização, Ms.c. thesis, Federal University of Rio de Janeiro/COPPE, Rio de Janeiro, Brazil (1982). [Google Scholar]
  • A.E. Xavier, Penalização Hiperbólica, Ph.D. thesis, Federal University of Rio de Janeiro/COPPE, Rio de Janeiro, Brazil (1992). [Google Scholar]
  • A.E. Xavier, Hyperbolic penalty: a new method for nonlinear programming with inequalities. Int. Trans. Oper. Res. 8 (2001) 659–671. [CrossRef] [MathSciNet] [Google Scholar]
  • A.E. Xavier, The hyperbolic smoothing clustering method. Pattern Recognit. 43 (2010) 731–737. [CrossRef] [Google Scholar]
  • A.E. Xavier, M.M. Gesteira and V.L. Xavier, Solving the continuous multiple allocation p-hub median problem by the hyperbolic smoothing approach. Optimization 64 (2015) 2631–2647. [CrossRef] [MathSciNet] [Google Scholar]
  • W.I. Zangwill, Non-linear programming via penalty functions. Manage. Sci. 13 (1967) 344–358. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.