The procedure for the interval evaluation of the 2 functions will be written as:

INTERVAL_VECTOR IntervalTestFunction (int l1,int l2,INTERVAL_VECTOR & in) // interval valued test function { INTERVAL x,y; INTERVAL_VECTOR xx(2); x=in(1); y=in(2); if(l1==1) xx(1)=Cos(x)+y*Sqr(Cos(y))-0.2; if(l1<=2 && l2>=2) xx(2)=Sqr(x)+Sqr(y); return xx; }while the main program may be written as:

int main() { int Iterations, Dimension,Dimension_Eq,Num,i,j,precision; double Accuracy,Accuracy_Variable; INTERVAL_MATRIX SolutionList(2,2); INTERVAL_VECTOR TestDomain(2),F(2),P(2),H(2); INTEGER_VECTOR Type(2); INTERVAL Optimum; REAL pi; pi=Constant::Pi; Dimension_Eq=2;Dimension=2; TestDomain(1)=INTERVAL(-pi,pi);TestDomain(2)=INTERVAL(-pi,pi); cerr << "Number of iteration = "; cin >> Iterations; cerr << "Accuracy on Function = "; cin >> Accuracy; Type(1)=0;Type(2)=-2; Accuracy=0; Num=Minimize_Maximize(Dimension,Dimension_Eq,Type, IntervalTestFunction,TestDomain,Iterations,Accuracy_Variable, Accuracy,0,Optimum,SolutionList); if(Num<0) { cout << "The procedure has failed, error code:"<<Num<<endl; return 0; } cout<<"Optimum:"<<Optimum<<" obtained at"<<endl; for(i=1;i<=Num;i++) { cout << "x=" << SolutionList(i,1) <<endl; cout << "y=" << SolutionList(i,2) <<endl; } return 0; }The

the

epsilonf |
Minimum | boxes | ||

0.01, DSM | [1.12195667, 1.12195667] | [-0.944932,-0.4786] | [-0.944932,-0.4786] | 76 (36) |

0.01, RSM | [1.12195667, 1.12195667] | [-0.944932,-0.4786] | [-0.944932,-0.4786] | 59 (37) |

0.001, DSM | [1.1401661,1.1401661] | [-0.954903,-0.477835] | [-0.954903,-0.477835] | 201 (75) |

0.001, RSM | [1.1401661,1.1401661] | [-0.954903,-0.477835] | [-0.954903,-0.477835] | 148 (67) |

0.000001, DSM | [1.14223267,1.14223267] | [-0.957596,-0.474596] | [-0.957596,-0.474596] | 5031 (2041) |

0.000001, RSM | [1.14223267,1.14223267] | [-0.957596,-0.474596] | [-0.957596,-0.474596] | 4590 (2164) |