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Diffstat (limited to 'demos')
-rw-r--r-- | demos/intfmincon.dem.sce | 136 | ||||
-rw-r--r-- | demos/intfminimax.dem.sce | 57 |
2 files changed, 193 insertions, 0 deletions
diff --git a/demos/intfmincon.dem.sce b/demos/intfmincon.dem.sce new file mode 100644 index 0000000..ef43b4b --- /dev/null +++ b/demos/intfmincon.dem.sce @@ -0,0 +1,136 @@ +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 =========// diff --git a/demos/intfminimax.dem.sce b/demos/intfminimax.dem.sce new file mode 100644 index 0000000..db74b92 --- /dev/null +++ b/demos/intfminimax.dem.sce @@ -0,0 +1,57 @@ +mode(1) +// +// Demo of intfminimax.sci +// + +// A basic case : +// we provide only the objective function and the nonlinear constraint +// function +function f = myfun(x) +f(1)= 2*x(1)^2 + x(2)^2 - 48*x(1) - 40*x(2) + 304; //Objectives +f(2)= -x(1)^2 - 3*x(2)^2; +f(3)= x(1) + 3*x(2) -18; +f(4)= -x(1) - x(2); +f(5)= x(1) + x(2) - 8; +endfunction +// The initial guess +x0 = [0.1,0.1]; +// The expected solution : only 4 digits are guaranteed +xopt = [4 4] +fopt = [0 -64 -2 -8 0] +intcon = [1] +maxfopt = 0 +// Run fminimax +[x,fval,maxfval,exitflag] = intfminimax(myfun, x0,intcon) +// Press ENTER to continue +halt() // Press return to continue + +// A case where we provide the gradient of the objective +// functions and the Jacobian matrix of the constraints. +// The objective function and its gradient +function [f,G] = myfun(x) +f(1)= 2*x(1)^2 + x(2)^2 - 48*x(1) - 40*x(2) + 304; +f(2)= -x(1)^2 - 3*x(2)^2; +f(3)= x(1) + 3*x(2) -18; +f(4)= -x(1) - x(2); +f(5)= x(1) + x(2) - 8; +G = [ 4*x(1) - 48, -2*x(1), 1, -1, 1; +2*x(2) - 40, -6*x(2), 3, -1, 1; ]' +endfunction +// The nonlinear constraints +function [c,ceq,DC,DCeq] = confun(x) +// Inequality constraints +c = [1.5 + x(1)*x(2) - x(1) - x(2), -x(1)*x(2) - 10] +// No nonlinear equality constraints +ceq=[] +DC= [x(2)-1, -x(2); +x(1)-1, -x(1)]' +DCeq = []' +endfunction +// Test with both gradient of objective and gradient of constraints +minimaxOptions = list("GradObj","on","GradCon","on"); +// The initial guess +x0 = [0,10]; +intcon = [2] +// Run intfminimax +[x,fval,maxfval,exitflag] = intfminimax(myfun,x0,intcon,[],[],[],[],[],[], confun, minimaxOptions) +//========= E N D === O F === D E M O =========// |