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-mode(1)
-//
-// Demo of intfmincon.sci
-//
-
-//Find x in R^2 such that it minimizes:
-//f(x)= -x1 -x2/3
-//x0=[0,0]
-//constraint-1 (c1): x1 + x2 <= 2
-//constraint-2 (c2): x1 + x2/4 <= 1
-//constraint-3 (c3): x1 - x2 <= 2
-//constraint-4 (c4): -x1/4 - x2 <= 1
-//constraint-5 (c5): -x1 - x2 <= -1
-//constraint-6 (c6): -x1 + x2 <= 2
-//constraint-7 (c7): x1 + x2 = 2
-//Objective function to be minimised
-function [y,dy]=f(x)
-y=-x(1)-x(2)/3;
-dy= [-1,-1/3];
-endfunction
-//Starting point, linear constraints and variable bounds
-x0=[0 , 0];
-intcon = [1]
-A=[1,1 ; 1,1/4 ; 1,-1 ; -1/4,-1 ; -1,-1 ; -1,1];
-b=[2;1;2;1;-1;2];
-Aeq=[1,1];
-beq=[2];
-lb=[];
-ub=[];
-nlc=[];
-//Options
-options=list("GradObj", "on");
-//Calling Ipopt
-[x,fval,exitflag,grad,hessian] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options)
-// Press ENTER to continue
-halt()   // Press return to continue
- 
-//Find x in R^3 such that it minimizes:
-//f(x)= x1*x2 + x2*x3
-//x0=[0.1 , 0.1 , 0.1]
-//constraint-1 (c1): x1^2 - x2^2 + x3^2 <= 2
-//constraint-2 (c2): x1^2 + x2^2 + x3^2 <= 10
-//Objective function to be minimised
-function [y,dy]=f(x)
-y=x(1)*x(2)+x(2)*x(3);
-dy= [x(2),x(1)+x(3),x(2)];
-endfunction
-//Starting point, linear constraints and variable bounds
-x0=[0.1 , 0.1 , 0.1];
-intcon = [2]
-A=[];
-b=[];
-Aeq=[];
-beq=[];
-lb=[];
-ub=[];
-//Nonlinear constraints
-function [c,ceq,cg,cgeq]=nlc(x)
-c = [x(1)^2 - x(2)^2 + x(3)^2 - 2 , x(1)^2 + x(2)^2 + x(3)^2 - 10];
-ceq = [];
-cg=[2*x(1) , -2*x(2) , 2*x(3) ; 2*x(1) , 2*x(2) , 2*x(3)];
-cgeq=[];
-endfunction
-//Options
-options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", "on","GradCon", "on");
-//Calling Ipopt
-[x,fval,exitflag,output] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options)
-// Press ENTER to continue
-halt()   // Press return to continue
- 
-//The below problem is an unbounded problem:
-//Find x in R^3 such that it minimizes:
-//f(x)= -(x1^2 + x2^2 + x3^2)
-//x0=[0.1 , 0.1 , 0.1]
-//  x1 <= 0
-//  x2 <= 0
-//  x3 <= 0
-//Objective function to be minimised
-function y=f(x)
-y=-(x(1)^2+x(2)^2+x(3)^2);
-endfunction
-//Starting point, linear constraints and variable bounds
-x0=[0.1 , 0.1 , 0.1];
-intcon = [3]
-A=[];
-b=[];
-Aeq=[];
-beq=[];
-lb=[];
-ub=[0,0,0];
-//Options
-options=list("MaxIter", [1500], "CpuTime", [500]);
-//Calling Ipopt
-[x,fval,exitflag,grad,hessian] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,[],options)
-// Press ENTER to continue
-halt()   // Press return to continue
- 
-//The below problem is an infeasible problem:
-//Find x in R^3 such that in minimizes:
-//f(x)=x1*x2 + x2*x3
-//x0=[1,1,1]
-//constraint-1 (c1): x1^2 <= 1
-//constraint-2 (c2): x1^2 + x2^2 <= 1
-//constraint-3 (c3): x3^2 <= 1
-//constraint-4 (c4): x1^3 = 0.5
-//constraint-5 (c5): x2^2 + x3^2 = 0.75
-// 0 <= x1 <=0.6
-// 0.2 <= x2 <= inf
-// -inf <= x3 <= 1
-//Objective function to be minimised
-function [y,dy]=f(x)
-y=x(1)*x(2)+x(2)*x(3);
-dy= [x(2),x(1)+x(3),x(2)];
-endfunction
-//Starting point, linear constraints and variable bounds
-x0=[1,1,1];
-intcon = [2]
-A=[];
-b=[];
-Aeq=[];
-beq=[];
-lb=[0 0.2,-%inf];
-ub=[0.6 %inf,1];
-//Nonlinear constraints
-function [c,ceq,cg,cgeq]=nlc(x)
-c=[x(1)^2-1,x(1)^2+x(2)^2-1,x(3)^2-1];
-ceq=[x(1)^3-0.5,x(2)^2+x(3)^2-0.75];
-cg = [2*x(1),0,0;2*x(1),2*x(2),0;0,0,2*x(3)];
-cgeq = [3*x(1)^2,0,0;0,2*x(2),2*x(3)];
-endfunction
-//Options
-options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", "on","GradCon", "on");
-//Calling Ipopt
-[x,fval,exitflag,grad,hessian] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options)
-// Press ENTER to continue
-//========= E N D === O F === D E M O =========//