# AMPL Model by Hande Y. Benson
#
# Copyright (C) 2001 Princeton University
# All Rights Reserved
#
# Permission to use, copy, modify, and distribute this software and
# its documentation for any purpose and without fee is hereby
# granted, provided that the above copyright notice appear in all
# copies and that the copyright notice and this
# permission notice appear in all supporting documentation.                     

#   Source: problem 12 in
#   P.T. Boggs and J.W. Tolle,
#   "A strategy for global convergence in a sequential 
#    quadratic programming algorithm",
#   SINUM 26(3), pp. 600-623, 1989.

#   The problem is not convex.

#   SIF input: Ph. Toint, June 1993.

#   classification QQR2-AN-5-3

param xinit{1..5};
var x{i in 1..5} := xinit[i];

minimize f:
	0.01*x[1]^2+x[2]^2;
subject to cons1:
	x[1]+x[2]-x[3]^2 = 25.0;
subject to cons2:
	x[1]^2+x[2]^2-x[4]^2 = 25.0;
subject to cons3:
	x[1]-x[5]^2 = 2.0;

data;
param xinit:=
1	15.811
2	1.5811
3	0.0
4	15.083
5	3.7164;

solve; display f; display x;