Open Access
Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
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Page(s) | 2941 - 2950 | |
DOI | https://doi.org/10.1051/ro/2023153 | |
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]
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