*************************** * SET UP THE INITIAL DATA * *************************** NAME GENROSE * Problem : * -------- * The generalized Rosenbrock function. * Source: problem 5 in * S. Nash, * "Newton-type minimization via the Lanczos process", * SIAM J. Num. Anal. 21, 1984, 770-788. * SIF input: Nick Gould, Oct 1992. * minor correction by Ph. Shott, Jan 1995. * classification SUR2-AN-V-0 * Number of variables *IE N 5 *IE N 10 *IE N 100 IE N 500 * other parameter definitions IE 1 1 IE 2 2 IA N-1 N -1 IA N+1 N 1 RI RN+1 N+1 VARIABLES DO I 1 N X X(I) ND GROUPS N OBJ DO I 2 N XN Q(I) 'SCALE' 0.01 XN Q(I) X(I) 1.0 XN L(I) X(I) 1.0 ND CONSTANTS GENROSE OBJ -1.0 DO I 2 N X GENROSE L(I) 1.0 ND BOUNDS FR GENROSE 'DEFAULT' START POINT * start with X(I) = I/N+1. DO I 1 N RI RI I R/ T RI RN+1 ZV GENROSE X(I) T ND ELEMENT TYPE EV MSQR V ELEMENT USES XT 'DEFAULT' MSQR DO I 2 N IA I-1 I -1 ZV Q(I) V X(I-1) ND GROUP TYPE GV L2 GVAR GROUP USES XT 'DEFAULT' L2 DO I 2 N XE Q(I) Q(I) ND OBJECT BOUND LO GENROSE 1.0 * Solution *LO SOLTN 1.0 ENDATA *********************** * SET UP THE FUNCTION * * AND RANGE ROUTINES * *********************** ELEMENTS GENROSE INDIVIDUALS T MSQR F - V ** 2 G V - 2.0D+0 * V H V V - 2.0D+0 ENDATA ********************* * SET UP THE GROUPS * * ROUTINE * ********************* GROUPS GENROSE INDIVIDUALS T L2 F GVAR * GVAR G GVAR + GVAR H 2.0 ENDATA