Merlin-3.0. A multidimensional optimization environment

We present an optimization environment for multidimensional continuous functions. Robust and powerful algorithms are used that guarantee its effectiveness. The environment offers programmability and ease of use by providing a specialized operating system and a control language that can be used to create successful optimization strategies. We report on several applications where this software has been successfully used.

[1]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[2]  William C. Davidon,et al.  Variable Metric Method for Minimization , 1959, SIAM J. Optim..

[3]  R. Fletcher,et al.  An efficient line search for nonlinear least squares , 1986 .

[4]  Jorge J. Moré,et al.  User Guide for Minpack-1 , 1980 .

[5]  J. Dennis,et al.  Two new unconstrained optimization algorithms which use function and gradient values , 1979 .

[6]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[7]  P. Wolfe.  Convergence Conditions for Ascent Methods. II , 1969 .

[8]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[9]  F. James,et al.  RANLUX: A Fortran implementation of the high-quality pseudorandom number generator of Lüscher , 1994 .

[10]  G. R. Hext,et al.  Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation , 1962 .

[11]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm , 1970 .

[12]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[13]  M. Powell.  Optimization in action: 7th–9th January 1975. University of Bristol, UK. Organized by the Institute of Mathematics and its Applications, Essex, UK , 1975 .

[14]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[15]  D. Shanno.  Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[16]  C. Storey,et al.  Generalized Polak-Ribière algorithm , 1992 .

[17]  A. Goldstein.  On Steepest Descent , 1965 .

[18]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[19]  Dimitris G. Papageorgiou,et al.  MERLIN-2.0 — Enhanced and programmable version , 1989 .

[20]  M. J. D. Powell,et al.  A tolerant algorithm for linearly constrained optimization calculations , 1989, Math. Program..

[21]  Dimitris G. Papageorgiou,et al.  MERLIN-2.1 double precision , 1990 .

[22]  W. Murray.  Numerical Methods for Unconstrained Optimization , 1975 .

[23]  Dimitris G. Papageorgiou,et al.  The Merlin control language for strategic optimization , 1998 .

[24]  D. Goldfarb.  A family of variable-metric methods derived by variational means , 1970 .

[25]  R. Schnabel,et al.  A view of unconstrained optimization , 1989 .

[26]  Ioannis N. Demetropoulos,et al.  Merlin - a portable system for multidimensional minimization , 1987 .

[27]  D. Fotiadis,et al.  Artificial neural network methods in quantum mechanics , 1997, quant-ph/9705029.

[28]  Donald Goldfarb,et al.  A numerically stable dual method for solving strictly convex quadratic programs , 1983, Math. Program..

[29]  Dimitris A. Karras,et al.  A novel neural network training technique based on a multi-algorithm constrained optimization strategy , 1998, Proceedings. 24th EUROMICRO Conference (Cat. No.98EX204).

[30]  Dimitris G. Papageorgiou,et al.  MCL — Optimization oriented programming language , 1989 .

[31]  Dimitris A. Karras,et al.  Neural network training and simulation using a multidimensional optimization system , 1998, Int. J. Comput. Math..

[32]  Dimitris G. Papageorgiou,et al.  How many conformers of the 1, 2, 3-propanetriol triacetate are present in gas phase and in aqueous solution? , 1996 .

[33]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[34]  Philip E. Gill,et al.  Practical optimization , 1981 .