On the Number of Inner Iterations Per Outer Iteration of a Globally Convergent Algorithm for Optimization with General Nonlinear Inequality Constraints and Simple Bounds

1. D. P. Bertsekas. Constrained Optimization and Lagrange Multiplier Methods. Academic Press, London, 1982.

   Google Scholar 

2. J. V. Burke and J. J. Moré. On the identification of active constraints. SIAM Journal on Numerical Analysis, 25(5):1197–1211, 1988.

   Google Scholar 

3. J. V. Burke, J. J. Moré, and G. Toraldo. Convergence properties of trust region methods for linear and convex constraints. Mathematical Programming, Series A, 47(3):305–336, 1990.

   Google Scholar 

4. P. H. Calamai and J. J. Moré. Projected gradient methods for linearly constrained problems. Mathematical Programming, 39:93–116, 1987.

   Google Scholar 

5. A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM Journal on Numerical Analysis, 25:433–460, 1988. See also same journal 26:764-767, 1989.

   Google Scholar 

6. A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Testing a class of methods for solving minimization problems with simple bounds on the variables. Mathematics of Computation, 50:399–430, 1988.

   Google Scholar 

7. A. R. Conn, N. I. M. Gould, and Ph. L. Toint. LANCELOT: a Fortran package for large-scale nonlinear Optimization (Release A). Number 17 in Springer Series in Computational Mathematics. Springer Verlag, Heidelberg, Berlin, New York, 1992.

   Google Scholar 

8. A. R. Conn, N. I. M. Gould, and Ph. L. Toint. On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear equality constraints and simple bounds. In D.F Griffiths and G.A. Watson, editors, Proceedings of the 14th Biennal Numerical Analysis Conference Dundee 1991, pages 49–68. Longmans, 1992.

9. A. R. Conn, N. I. M. Gould, and Ph. L. Toint. A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds. Mathematics of Computation, volume 66, pages 261–288, 1997.

   Google Scholar 

10. J. E. Dennis and J. J. Moré. A characterization of superlinear convergence and its application to quasi-Newton methods. Mathematics of Computation, 28(126):549–560, 1974.

    Google Scholar 

11. J. E. Dennis and R. B. Schnabel. Numerical methods for unconstrained Optimization and nonlinear equations. Prentice-Hall, Englewood Cliffs, USA, 1983.

    Google Scholar 

12. A. V. Fiacco and G. P. McCormick. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. J. Wiley and Sons, New York, 1968. Reprinted as Classics in Applied Mathematics 4, SIAM, 1990.

    Google Scholar 

13. N. I. M. Gould. On the accurate determination of search directions for simple differentiable penalty functions. IMA Journal of Numerical Analysis, 6:357–372, 1986.

    Google Scholar 

14. N. I. M. Gould. On the convergence of a sequential penalty function method for constrained minimization. SIAM Journal on Numerical Analysis, 26:107–128, 1989.

    Google Scholar 

15. J. J. Moré. Trust regions and projected gradients. In M. Iri and K. Yajima, editors, System Modelling and Optimization, volume 113, pages 1–13, Berlin, 1988. Springer Verlag. Lecture Notes in Control and Information Sciences.

16. Ph. L. Toint. Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space. IMA Journal of Numerical Analysis, 8:231–252, 1988.

    Google Scholar 

17. M. H. Wright. Interior methods for constrained optimization. volume 1 of Acta Numerica, pages 341–407. Cambridge University Press, New York, 1992.

    Google Scholar 

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