functions added

7 files changed, 503 insertions, 0 deletions

diff --git a/demos/exmip1.mps b/demos/exmip1.mps
new file mode 100644
index 0000000..4f73ac5
--- /dev/null
+++ b/demos/exmip1.mps
@@ -0,0 +1,70 @@
+************************************************************************        
+*                                                                               
+*  The data in this file represents the following problem:                      
+*                                                                               
+*  Minimize or maximize Z = x1 + 2x5 - x8                                       
+*                                                                               
+*  Subject to:                                                                  
+*                                                                               
+*  2.5 <=   3x1 +  x2         -  2x4 - x5               -    x8                 
+*                 2x2 + 1.1x3                                   <=  2.1         
+*                          x3              +  x6                 =  4.0         
+*  1.8 <=                      2.8x4             -1.2x7         <=  5.0         
+*  3.0 <= 5.6x1                      + x5               + 1.9x8 <= 15.0         
+*                                                                               
+*  where:                                                                       
+*                                                                               
+*  2.5 <= x1                                                                    
+*    0 <= x2 <= 4.1                                                             
+*    0 <= x3                                                                    
+*    0 <= x4                                                                    
+*  0.5 <= x5 <= 4.0                                                             
+*    0 <= x6                                                                    
+*    0 <= x7                                                                    
+*    0 <= x8 <= 4.3                                                             
+*                                                                               
+*  x3, x4 are 0,1 variables.                                                    
+*                                                                               
+************************************************************************        
+NAME          EXAMPLE                                                           
+ROWS                                                                            
+ N  OBJ                                                                         
+ G  ROW01                                                                       
+ L  ROW02                                                                       
+ E  ROW03                                                                       
+ G  ROW04                                                                       
+ L  ROW05                                                                       
+COLUMNS                                                                         
+    COL01     OBJ                1.0                                            
+    COL01     ROW01              3.0   ROW05              5.6                   
+    COL02     ROW01              1.0   ROW02              2.0                   
+*                                                                               
+*  Mark COL03 and COL04 as integer variables.                                   
+*                                                                               
+    INT1      'MARKER'                 'INTORG'                                 
+    COL03     ROW02              1.1   ROW03              1.0                   
+    COL04     ROW01             -2.0   ROW04              2.8                   
+    INT1END   'MARKER'                 'INTEND'                                 
+*                                                                               
+    COL05     OBJ                2.0                                            
+    COL05     ROW01             -1.0   ROW05              1.0                   
+    COL06     ROW03              1.0                                            
+    COL07     ROW04             -1.2                                            
+    COL08     OBJ               -1.0                                            
+    COL08     ROW01             -1.0   ROW05              1.9                   
+RHS                                                                             
+    RHS1      ROW01              2.5                                            
+    RHS1      ROW02              2.1                                            
+    RHS1      ROW03              4.0                                            
+    RHS1      ROW04              1.8                                            
+    RHS1      ROW05             15.0                                            
+RANGES                                                                          
+    RNG1      ROW04              3.2                                            
+    RNG1      ROW05             12.0                                            
+BOUNDS                                                                          
+ LO BND1      COL01              2.5                                            
+ UP BND1      COL02              4.1                                            
+ LO BND1      COL05              0.5                                            
+ UP BND1      COL05              4.0                                            
+ UP BND1      COL08              4.3                                            
+ENDATA                                                                          
diff --git a/demos/fgoalattain.dem.sce b/demos/fgoalattain.dem.sce
new file mode 100644
index 0000000..89a5957
--- /dev/null
+++ b/demos/fgoalattain.dem.sce
@@ -0,0 +1,26 @@
+mode(1)
+//
+// Demo of fgoalattain.sci
+//
+
+function f1 = fun(x)
+f1(1)=2*x(1)*x(1)+x(2)*x(2)-48*x(1)-40*x(2)+304
+f1(2)=-x(1)*x(1)-3*x(2)*x(2)
+f1(3)=x(1)+3*x(2)-18
+f1(4)=-x(1)-x(2)
+f1(5)=x(1)+x(2)-8
+endfunction
+x0=[-1,1];
+halt()   // Press return to continue
+ 
+goal=[-5,-3,-2,-1,-4];
+weight=abs(goal)
+//xopt  = [-0.0000011 -63.999998 -2.0000002 -8 3.485D-08]
+//fval  = [4 3.99]
+halt()   // Press return to continue
+ 
+//Run fgoalattain
+[xopt,fval,attainfactor,exitflag,output,lambda]=fgoalattain(fun,x0,goal,weight)
+halt()   // Press return to continue
+ 
+//========= E N D === O F === D E M O =========//
diff --git a/demos/fminbnd.dem.sce b/demos/fminbnd.dem.sce
new file mode 100644
index 0000000..a9b4865
--- /dev/null
+++ b/demos/fminbnd.dem.sce
@@ -0,0 +1,54 @@
+mode(1)
+//
+// Demo of fminbnd.sci
+//
+
+//Find x in R^6 such that it minimizes:
+//f(x)= sin(x1) + sin(x2) + sin(x3) + sin(x4) + sin(x5) + sin(x6)
+//-2 <= x1,x2,x3,x4,x5,x6 <= 2
+//Objective function to be minimised
+function y=f(x)
+y=0
+for i =1:6
+y=y+sin(x(i));
+end
+endfunction
+//Variable bounds
+x1 = [-2, -2, -2, -2, -2, -2];
+x2 = [2, 2, 2, 2, 2, 2];
+//Options
+options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6])
+//Calling Ipopt
+[x,fval] =fminbnd(f, x1, x2, options)
+halt()   // Press return to continue
+ 
+//Find x in R such that it minimizes:
+//f(x)= 1/x^2
+//0 <= x <= 1000
+//Objective function to be minimised
+function y=f(x)
+y=1/x^2
+endfunction
+//Variable bounds
+x1 = [0];
+x2 = [1000];
+//Calling Ipopt
+[x,fval,exitflag,output,lambda] =fminbnd(f, x1, x2)
+halt()   // Press return to continue
+ 
+//The below problem is an unbounded problem:
+//Find x in R^2 such that it minimizes:
+//f(x)= -[(x1-1)^2 + (x2-1)^2]
+//-inf <= x1,x2 <= inf
+//Objective function to be minimised
+function y=f(x)
+y=-((x(1)-1)^2+(x(2)-1)^2);
+endfunction
+//Variable bounds
+x1 = [-%inf , -%inf];
+x2 = [];
+//Options
+options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6])
+//Calling Ipopt
+[x,fval,exitflag,output,lambda] =fminbnd(f, x1, x2, options)
+//========= E N D === O F === D E M O =========//
diff --git a/demos/fmincon.dem.sce b/demos/fmincon.dem.sce
new file mode 100644
index 0000000..790c67f
--- /dev/null
+++ b/demos/fmincon.dem.sce
@@ -0,0 +1,155 @@
+mode(1)
+//
+// Demo of fmincon.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=f(x)
+y=-x(1)-x(2)/3;
+endfunction
+//Starting point, linear constraints and variable bounds
+x0=[0 , 0];
+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=[];
+//Gradient of objective function
+function y= fGrad(x)
+y= [-1,-1/3];
+endfunction
+//Hessian of lagrangian
+function y= lHess(x,obj,lambda)
+y= obj*[0,0;0,0]
+endfunction
+//Options
+options=list("GradObj", fGrad, "Hessian", lHess);
+//Calling Ipopt
+[x,fval,exitflag,output,lambda,grad,hessian] =fmincon(f, x0,A,b,Aeq,beq,lb,ub,nlc,options)
+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=f(x)
+y=x(1)*x(2)+x(2)*x(3);
+endfunction
+//Starting point, linear constraints and variable bounds
+x0=[0.1 , 0.1 , 0.1];
+A=[];
+b=[];
+Aeq=[];
+beq=[];
+lb=[];
+ub=[];
+//Nonlinear constraints
+function [c,ceq]=nlc(x)
+c = [x(1)^2 - x(2)^2 + x(3)^2 - 2 , x(1)^2 + x(2)^2 + x(3)^2 - 10];
+ceq = [];
+endfunction
+//Gradient of objective function
+function y= fGrad(x)
+y= [x(2),x(1)+x(3),x(2)];
+endfunction
+//Hessian of the Lagrange Function
+function y= lHess(x,obj,lambda)
+y= obj*[0,1,0;1,0,1;0,1,0] + lambda(1)*[2,0,0;0,-2,0;0,0,2] + lambda(2)*[2,0,0;0,2,0;0,0,2]
+endfunction
+//Gradient of Non-Linear Constraints
+function [cg,ceqg] = cGrad(x)
+cg=[2*x(1) , -2*x(2) , 2*x(3) ; 2*x(1) , 2*x(2) , 2*x(3)];
+ceqg=[];
+endfunction
+//Options
+options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", fGrad, "Hessian", lHess,"GradCon", cGrad);
+//Calling Ipopt
+[x,fval,exitflag,output] =fmincon(f, x0,A,b,Aeq,beq,lb,ub,nlc,options)
+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];
+A=[];
+b=[];
+Aeq=[];
+beq=[];
+lb=[];
+ub=[0,0,0];
+//Options
+options=list("MaxIter", [1500], "CpuTime", [500]);
+//Calling Ipopt
+[x,fval,exitflag,output,lambda,grad,hessian] =fmincon(f, x0,A,b,Aeq,beq,lb,ub,[],options)
+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=f(x)
+y=x(1)*x(2)+x(2)*x(3);
+endfunction
+//Starting point, linear constraints and variable bounds
+x0=[1,1,1];
+A=[];
+b=[];
+Aeq=[];
+beq=[];
+lb=[0 0.2,-%inf];
+ub=[0.6 %inf,1];
+//Nonlinear constraints
+function [c,ceq]=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];
+endfunction
+//Gradient of objective function
+function y= fGrad(x)
+y= [x(2),x(1)+x(3),x(2)];
+endfunction
+//Hessian of the Lagrange Function
+function y= lHess(x,obj,lambda)
+y= obj*[0,1,0;1,0,1;0,1,0] + lambda(1)*[2,0,0;0,0,0;0,0,0] + lambda(2)*[2,0,0;0,2,0;0,0,0] +lambda(3)*[0,0,0;0,0,0;0,0,2] + lambda(4)*[6*x(1    ),0,0;0,0,0;0,0,0] + lambda(5)*[0,0,0;0,2,0;0,0,2];
+endfunction
+//Gradient of Non-Linear Constraints
+function [cg,ceqg] = cGrad(x)
+cg = [2*x(1),0,0;2*x(1),2*x(2),0;0,0,2*x(3)];
+ceqg = [3*x(1)^2,0,0;0,2*x(2),2*x(3)];
+endfunction
+//Options
+options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", fGrad, "Hessian", lHess,"GradCon", cGrad);
+//Calling Ipopt
+[x,fval,exitflag,output,lambda,grad,hessian] =fmincon(f, x0,A,b,Aeq,beq,lb,ub,nlc,options)
+//========= E N D === O F === D E M O =========//
diff --git a/demos/fminimax.dem.sce b/demos/fminimax.dem.sce
new file mode 100644
index 0000000..404af00
--- /dev/null
+++ b/demos/fminimax.dem.sce
@@ -0,0 +1,73 @@
+mode(1)
+//
+// Demo of fminimax.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]
+maxfopt = 0
+// Run fminimax
+[xopt,fopt,maxfval,exitflag,output,lambda] = fminimax(myfun, x0)
+// 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 = 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;
+endfunction
+// Defining gradient of myfun
+function G = myfungrad(x)
+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 and the Jacobian
+// matrix of the constraints
+function [c,ceq] = 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=[]
+endfunction
+// Defining gradient of confungrad
+function [DC,DCeq] = cgrad(x)
+// DC(:,i) = gradient of the i-th constraint
+// DC = [
+//   Dc1/Dx1  Dc1/Dx2
+//   Dc2/Dx1  Dc2/Dx2
+//   ]
+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",myfungrad,"GradCon",cgrad);
+// The initial guess
+x0 = [0,10];
+// The expected solution : only 4 digits are guaranteed
+//xopt = [0.92791 7.93551]
+//fopt = [6.73443  -189.778  6.73443  -8.86342  0.86342]
+maxfopt = 6.73443
+// Run fminimax
+[xopt,fopt,maxfval,exitflag,output] = fminimax(myfun,x0,[],[],[],[],[],[], confun, minimaxOptions)
+//========= E N D === O F === D E M O =========//
diff --git a/demos/fminunc.dem.sce b/demos/fminunc.dem.sce
new file mode 100644
index 0000000..80eed72
--- /dev/null
+++ b/demos/fminunc.dem.sce
@@ -0,0 +1,61 @@
+mode(1)
+//
+// Demo of fminunc.sci
+//
+
+//Find x in R^2 such that it minimizes the Rosenbrock function
+//f = 100*(x2 - x1^2)^2 + (1-x1)^2
+//Objective function to be minimised
+function y= f(x)
+y= 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;
+endfunction
+//Starting point
+x0=[-1,2];
+//Gradient of objective function
+function y= fGrad(x)
+y= [-400*x(1)*x(2) + 400*x(1)^3 + 2*x(1)-2, 200*(x(2)-x(1)^2)];
+endfunction
+//Hessian of Objective Function
+function y= fHess(x)
+y= [1200*x(1)^2- 400*x(2) + 2, -400*x(1);-400*x(1), 200 ];
+endfunction
+//Options
+options=list("MaxIter", [1500], "CpuTime", [500], "Gradient", fGrad, "Hessian", fHess);
+//Calling Ipopt
+[xopt,fopt,exitflag,output,gradient,hessian]=fminunc(f,x0,options)
+halt()   // Press return to continue
+ 
+//Find x in R^2 such that the below function is minimum
+//f = x1^2 + x2^2
+//Objective function to be minimised
+function y= f(x)
+y= x(1)^2 + x(2)^2;
+endfunction
+//Starting point
+x0=[2,1];
+//Calling Ipopt
+[xopt,fopt]=fminunc(f,x0)
+halt()   // Press return to continue
+ 
+//The below problem is an unbounded problem:
+//Find x in R^2 such that the below function is minimum
+//f = - x1^2 - x2^2
+//Objective function to be minimised
+function y= f(x)
+y= -x(1)^2 - x(2)^2;
+endfunction
+//Starting point
+x0=[2,1];
+//Gradient of objective function
+function y= fGrad(x)
+y= [-2*x(1),-2*x(2)];
+endfunction
+//Hessian of Objective Function
+function y= fHess(x)
+y= [-2,0;0,-2];
+endfunction
+//Options
+options=list("MaxIter", [1500], "CpuTime", [500], "Gradient", fGrad, "Hessian", fHess);
+//Calling Ipopt
+[xopt,fopt,exitflag,output,gradient,hessian]=fminunc(f,x0,options)
+//========= E N D === O F === D E M O =========//
diff --git a/demos/linprog.dem.sce b/demos/linprog.dem.sce
new file mode 100755
index 0000000..337a5dc
--- /dev/null
+++ b/demos/linprog.dem.sce
@@ -0,0 +1,64 @@
+mode(1)
+//
+// Demo of linprog.sci
+//
+
+//Optimal problems
+//Linear program, linear inequality constraints
+c=[-1,-1/3]'
+A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
+b=[2,1,2,1,-1,2]
+[xopt,fopt,exitflag,output,lambda]=linprog(c, A, b)
+// Press ENTER to continue
+halt()   // Press return to continue
+ 
+//Linear program with Linear Inequalities and Equalities`
+c=[-1,-1/3]'
+A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
+b=[2,1,2,1,-1,2]
+Aeq=[1,1/4]
+beq=[1/2]
+[xopt,fopt,exitflag,output,lambda]=linprog(c, A, b, Aeq, beq)
+// Press ENTER to continue
+halt()   // Press return to continue
+ 
+//Linear program with all constraint types
+c=[-1,-1/3]'
+A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
+b=[2,1,2,1,-1,2]
+Aeq=[1,1/4]
+beq=[1/2]
+lb=[-1,-0.5]
+ub=[1.5,1.25]
+[xopt,fopt,exitflag,output,lambda]=linprog(c, A, b, Aeq, beq, lb, ub)
+// Press ENTER to continue
+halt()   // Press return to continue
+ 
+//Primal Infeasible Problem
+c=[-1,-1,-1]'
+A=[1,2,-1]
+b=[-4]
+Aeq=[1,5,3;1,1,0]
+beq=[10,100]
+lb=[0,0,0]
+ub=[%inf,%inf,%inf]
+[xopt,fopt,exitflag,output,lambda]= linprog(c,A,b,Aeq,beq,lb,ub)
+// Press ENTER to continue
+halt()   // Press return to continue
+ 
+//Dual Infeasible Problem
+c=[3,5,-7]'
+A=[-1,-1,4;1,1,4]
+b=[-8,5]
+Aeq=[]
+beq=[]
+lb=[-%inf,-%inf,-%inf]
+ub=[%inf,%inf,%inf]
+[xopt,fopt,exitflag,output,lambda]= linprog(c,A,b,Aeq,beq,lb,ub)
+// Press ENTER to continue
+halt()   // Press return to continue
+ 
+filepath = get_absolute_file_path('linprog.dem.sce');
+filepath = filepath + "exmip1.mps"
+[xopt,fopt,exitflag,output,lambda] =linprog(filepath);
+//========= E N D === O F === D E M O =========//