Conn, A.R., Gould, N.I.M. and Toint, Ph.L. A note on exploiting structure when using slack variables. Mathematical Programming, 67(1):89-97, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....performs poorly arises if many inequality constraints are present. This is due to the fact that it adds a slack variable for each inequality. Thus the OET problems which have n = 5 variables and m = 1002 constraints become problems in 1007 variables for LANCELOT. A remedy for this is provided in [3]. We also observed that lter SQP outperforms LANCELOT on problems with many equations. By switching to a genuine feasibility restoration phase, lter SQP exhibits fast local convergence even if the NLP problem is (locally) inconsistent. Of course the performance of LANCELOT can also be improved ....

Conn, A.R., Gould, N.I.M. and Toint, Ph.L. A note on exploiting structure when using slack variables. Mathematical Programming, 67(1):89-97, 1994.

....as well as certain relevant techniques in common with unconstrained optimization codes, were put into perspective, and several new techniques were proposed. Salient among these was transformation of inequality constraints into a combination of equality constraints and bound constraints, as in [3], combined with a process of handling bound constraints with reduced gradients and the peeling process that first appeared in [17] It has recently become apparent that branch and bound methods for nonlinear equations and for nonlinear optimization benefit from use of a floating point code to ....

Conn, A. R., Gould, N., and Toint, Ph. L., A Note on Exploiting Structure when using Slack Variables, Math. Prog. 67 (1), pp. 89--99, 1994.

.... 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 ....

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A. R. Conn, Nick Gould, and Ph. L. Toint. A note on exploiting structure when using slack variables. Research Report RC 18435, IBM T. J. Watson Research Center, Yorktown Heights, USA, 1992.

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