Convergence to Second-Order Stationary Points of a Primal-Dual Algorithm Model for Nonlinear Programming

References

• Auslender A. Penalty methods for computing points that satisfy second order necessary conditions. Math. Programming (1979) 17:229–238Crossref, Google Scholar
• Byrd R. H., Hribar M. E., Nocedal J. An interior point algorithm for large-scale nonlinear programming. SIAM J. Optim. (1999) 9:877–900Crossref, Google Scholar
• Byrd R. H., Schnabel R. B., Shultz G. A. A trust region algorithm for nonlinearly constrained optimization. SIAM J. Numer. Anal. (1987) 24:1152–1170Crossref, Google Scholar
• Clarke F. H.Optimization and Nonsmooth Analysis (1983) (John Wiley and Sons, New York) Google Scholar
• Coleman T. F., Liu J., Yuan W. A new trust-region algorithm for equality constrained optimization. Comput. Optim. Appl. (2002) 21:177–199Crossref, Google Scholar
• Conn A. R., Gould N. I. M., Orban D., Toint Ph. L. A primal-dual trust region algorithm for non-convex nonlinear programming. Math. Programming Ser. B (2000) 87:215–249Crossref, Google Scholar
• Dennis J. E., Vicente L. N. On the convergence theory of trust-region-based algorithms for equality-constrained optimization. SIAM J. Optim. (1997) 7:527–550Crossref, Google Scholar
• Dennis J. E., Heinkenschloss M., Vicente L. N. Trust-region interior-point SQP algorithms for a class of nonlinear programming problems. SIAM J. Control Optim. (1998) 36:1750–1794Crossref, Google Scholar
• Di Pillo G., Grippo L. Exact penalty functions in constrained optimization. SIAM J. Control Optim. (1989) 27:1333–1360Crossref, Google Scholar
• Di Pillo G., Lucidi S., Di Pillo G., Giannessi F. On exact augmented Lagrangian functions in nonlinear programming. Nonlinear Optimization and Applications (1996) (Plenum Press, New York) 85–100Crossref, Google Scholar
• Di Pillo G., Lucidi S. An augmented Lagrangian function with improved exactness properties. SIAM J. Optim. (2001) 12:376–406Crossref, Google Scholar
• Di Pillo G., Liuzzi G., Lucidi S., Palagi L. Use of a truncated Newton direction in an augmented Lagrangian framework. (2002) . Technical Report 18-02, Dipartimento di Informatica e Sistemistica, Università di Roma, “La Sapienza,” Rome, Italy http://www.dis.uniroma1.it/?palagiGoogle Scholar
• El-Alem M. Convergence to a second-order point for a trust-region algorithm with a nonmonotonic penalty parameter for constrained optimization. J. Optim. Theory Appl. (1996) 91:61–79Crossref, Google Scholar
• Facchinei F., Lucidi S. Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems. J. Optim. Theory Appl. (1995) 85:265–289Crossref, Google Scholar
• Facchinei F., Lucidi S. Convergence to second order stationary points in inequality constrained optimization. Math. Oper. Res. (1998) 23:746–766Link, Google Scholar
• Facchinei F., Fischer A., Kanzow C. On the accurate identification of active constraints. SIAM J. Optim. (1998) 9:14–32Crossref, Google Scholar
• Ferris M. C., Lucidi S., Roma M. Nonmonotone curvilinear line search methods for unconstrained optimization. Comput. Optim. Appl. (1996) 6:117–136Crossref, Google Scholar
• Forsgren A., Murray W. Newton methods for large-scale linear inequality constrained minimization. SIAM J. Optim. (1997) 7:162–176Crossref, Google Scholar
• Glad T., Polak E. A multiplier method with automatic limitation of penalty growth. Math. Programming (1979) 17:140–155Crossref, Google Scholar
• Grippo L., Lampariello F., Lucidi S. A truncated Newton method with nonmonotone linesearch for unconstrained optimization. J. Optim. Theory Appl. (1989) 60:401–419Crossref, Google Scholar
• Hiriart-Urruty J.-B., Strodiot J. J., Nguyen V. H. Generalized Hessian matrix and second-order optimality conditions for problems with C1, 1 data. Appl. Math. Optim. (1984) 11:43–56Crossref, Google Scholar
• Lucidi S. New results on a continuosly differentiable exact penalty function. SIAM J. Optim. (1992) 2:558–574Crossref, Google Scholar
• Lucidi S., Rochetich F., Roma M. Curvilinear stabilization techniques for truncated Newton methods in large scale unconstrained optimization: The complete results. SIAM J. Optim. (1998) 8:916–939Crossref, Google Scholar
• McCormick G. P. A modification of Armijo’s step-size rule for negative curvature. Math. Programming (1977) 13:111–115Crossref, Google Scholar
• McCormick G. P.Nonlinear Programming: Theory, Algorithms and Applications (1983) (John Wiley and Sons, New York) Google Scholar
• Moguerza J. M., Prieto F. J. An augmented Lagrangian interior point method using directions of negative curvature. Math. Programming (2003) 95:573–616Crossref, Google Scholar
• Moré J. J., Sorensen D. C. On the use of directions of negative curvature in a modified Newton method. Math. Programming (1979) 16:1–20Crossref, Google Scholar
• Moré J. J., Sorensen D. C. Computing a trust region step. SIAM J. Sci. Statist. Comput. (1983) 4:553–572Crossref, Google Scholar
• Mukai H., Polak E. A second-order method for the general nonlinear programming problem. J. Optim. Theory Appl. (1978) 26:515–532Crossref, Google Scholar
• Qi L., Sun J. A nonsmooth version of Newton’s method. Math. Programming (1993) 58:353–367Crossref, Google Scholar
• Sorensen D. C. Newton’s method with a model trust region modification. SIAM J. Numer. Anal. (1982) 19:409–426Crossref, Google Scholar
• Tseng P. A convergent infeasible interior-point trust-region methods for constrained optimization. SIAM J. Optim. (2002) 13:432–469Crossref, Google Scholar