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 Biennial Numerical Analysis Conference, Dundee, pp. 49-68, Longmans, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....feasibility set and finds an initial feasible point. The actual minimization is carried in Phase II. The Phase I relies on the availability of the bounding constants and tends to be numerically unstable if the constants involved are large. Several researchers have tried to overcome this problem [40, 41]. On the other hand, several alternate methods have been developed which do not require an initial feasible point (an example is the projected gradient method suggested in [25] Thus, as the research in interior point algorithms progresses, the set estimation problem can be solved more ....

A. R. Conn, N. Gould, and P. L. Toint, "On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds," Tech. Rep. RAL 92-068, Rutherford Appleton Laboratory, Oxfordshire, England, 1992.

....feasibility set and finds an initial feasible point. The actual minimization is carried in Phase II. The Phase I relies on the availability of the bounding constants and tends to be numerically unstable if the constants involved are large. Several researchers have tried to overcome this problem [40, 41]. On the other hand, several alternate methods have been developed which do not require an initial feasible point (an example is the projected gradient method suggested in [25] Thus, as the research in interior point algorithms progresses, the set estimation problem can be solved more ....

A. R. Conn, N. Gould, and P. L. Toint, "On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds," Tech. Rep. RAL 92-068, Rutherford Appleton Laboratory, Oxfordshire, England, 1992.

No context found.

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 Biennial Numerical Analysis Conference, Dundee, pp. 49-68, Longmans, 1992.

.... Duff and Reid (1983) and Duff and Reid (1993) By contrast, the sparse Cholesky factorization primarily tries to order the rows and columns of B whilst maintaining reasonable stability by including the possibility of adding appropriate quantities to the diagonals of B, if necessary, Chapter 3 of Conn et al. 1992b, Gill and Murray, 1974, Gill et al. 1992, Schlick, 1993 and Schnabel and Eskow, 1991) For example, Schnabel and Eskow use Gerschgorin bounds to determine the amount to add to the diagonal. They choose diagonal pivots and change the diagonal as little as is 5 reasonable in order to maintain ....

....provided one does at least as well as the generalized Cauchy point. One obtains better convergence, and ultimately a satisfactory asymptotic convergence rate, by further reducing the model function. This is the trust region basis for the kernel algorithm SBMIN (Conn et al. 1988a) of LANCELOT (Conn et al. 1992b) It can be summarized as follows: ffl Find the generalized Cauchy point based upon a local (quadratic) model. ffl Fix activities to those at the generalized Cauchy point. ffl (Approximately) solve the resulting reduced problem whilst maintaining account of the trust region and bounds. ffl ....

[Article contains additional citation context not shown here]

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 inequality constraints and simple bounds. Research Report RC 18382, IBM T. J. Watson Research Center, Yorktown Heights, USA, 1992.

.... we intend to determine conditions under which, asymptotically, a single Newton step is strictly feasible (in contrast with the purely primal case) and results in a point that satis es suitable barrier subproblem termination rules, after every reduction of the barrier parameter (see for instance [1, 3, 4] for previous work on the subject) This is shown to imply a componentwise Q superlinear rate of convergence, a stronger result than simply Q superlinear convergence of the vector of variables and Lagrange multipliers. Furthermore, this rate of convergence may be made arbitrarily close to ....

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 inequality constraints and simple bounds. Computational Optimization and Applications, 7(1):41-70, 1997.

....amongst others. Variations on the theme include the modified (unshifted) barrier function of Jittorntrum and Osborne (1980) the shifted barrier functions of Gill et al. 1988) and Freund (1991) the modified (shifted) barrier function of Polyak (1992) and the Lagrangian barrier function of Conn et al. 1992a) A typical barrier function method attempts to solve (1.1) by (approximately) minimizing a sequence of barrier functions 9(x; w (k) s (k) for appropriate sequences of weights fw (k) g and shifts fs (k) g. The approximate minimizer x (k) of 9(x; w (k) s (k) is generally ....

....small. We need to be cautious here as there is no guarantee that x (k) is feasible for the shifted constraints once the updates (4.30) 8 have been applied. It may then be necessary to find an alternative starting point for the k 1 st inner iteration. Suitable methods are given by Conn et al. 1992a) If the asymptotic phase of the algorithm is reached, the penalty parameter (k) remains fixed at some value 3 0 and the Lagrange multiplier estimates (k 1) are defined by (k 1) i = w (k) i c i (x (k) s (k) i ; for i = 1; m (4:32) c.f. 3.9) Here, the shifts ....

[Article contains additional citation context not shown here]

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 inequality constraints and simple bounds. Technical Report 92-068, Rutherford Appleton Laboratory, Chilton, Oxfordshire, England, 1992.

No context found.

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.

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