+
fgoalattain
+Solves a multiobjective goal attainment problem
Calling Sequence
+x = fgoalattain(fun,x0,goal,weight) +x = fgoalattain(fun,x0,goal,weight,A,b) +x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq) +x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub) +x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon) +x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,options) +[x,fval] = fgoalattain(...) +[x,fval,attainfactor] = fgoalattain(...) +[x,fval,attainfactor,exitflag] = fgoalattain(...) +[x,fval,attainfactor,exitflag,output] = fgoalattain(...) +[x,fval,attainfactor,exitflag,output,lambda] = fgoalattain(...)
Parameters
+- fun: +
a function that accepts a vector x and returns a vector F
+ - x0: +
a nx1 or 1xn matrix of double, where n is the number of variables.
+ - A: +
a nil x n matrix of double, where n is the number of variables and
+ - b: +
a nil x 1 matrix of double, where nil is the number of linear
+ - Aeq: +
a nel x n matrix of double, where n is the number of variables
+ - beq: +
a nel x 1 matrix of double, where nel is the number of linear
+ - lb: +
a nx1 or 1xn matrix of double, where n is the number of variables.
+ - ub: +
a nx1 or 1xn matrix of double, where n is the number of variables.
+ - nonlcon: +
a function, the nonlinear constraints
+ - options : +
a list, containing the option for user to specify. See below for details.
+ - x: +
a nx1 matrix of double, the computed solution of the optimization problem
+ - fval: +
a vector of double, the value of functions at x
+ - attainfactor: +
The amount of over- or underachievement of the goals,γ at the solution.
+ - exitflag: +
a 1x1 matrix of floating point integers, the exit status
+ - output: +
a struct, the details of the optimization process
+ - lambda: +
a struct, the Lagrange multipliers at optimum
Description
+fgoalattain solves the goal attainment problem, which is one formulation for minimizing a multiobjective optimization problem. +Finds the minimum of a problem specified by: +Minimise Y such that
+
The solver makes use of fmincon to find the minimum.
+The fgoalattain finds out the maximum value of Y for the objectives evaluated at the starting point and +adds that as another variable to the vector x +This is passed to the fmincon function to get the optimised value of Y +Hence, the algorithm used mainly is "ipopt" to obtain the optimum solution +The relations between f(x), Y, weights and goals are added as additional non-linear inequality constraints
+The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +
- Syntax : options= list("MaxIter", [---], "CpuTime", [---], "GradObj", ---, "GradCon", ---); +
- MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take. +
- CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take. +
- GradObj : a function, representing the gradient function of the Objective in Vector Form. +
- GradCon : a function, representing the gradient of the Non-Linear Constraints (both Equality and Inequality) of the problem. It is declared in such a way that gradient of non-linear inequality constraints are defined first as a separate Matrix (cg of size m2 X n or as an empty), followed by gradient of non-linear equality constraints as a separate Matrix (ceqg of size m2 X n or as an empty) where m2 & m3 are number of non-linear inequality and equality constraints respectively. +
- Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);
By default, the gradient options for fminimax are turned off and and fmincon does the gradient opproximation of minmaxObjfun. In case the GradObj option is off and GradConstr option is on, fminimax approximates minmaxObjfun gradient using numderivative toolbox.
+If we can provide exact gradients, we should do so since it improves the convergence speed of the optimization algorithm.
+Furthermore, we must enable the "GradObj" option with the statement : +
minimaxOptions = list("GradObj",fGrad); |  |  |
The constraint function must have header : +
[c, ceq] = confun(x) | | |
By default, the gradient options for fminimax are turned off and and fmincon does the gradient opproximation of confun. In case the GradObj option is on and GradCons option is off, fminimax approximates confun gradient using numderivative toolbox.
+If we can provide exact gradients, we should do so since it improves the convergence speed of the optimization algorithm.
+Furthermore, we must enable the "GradCon" option with the statement : +
minimaxOptions = list("GradCon",confunGrad); | | |
The constraint derivative function must have header : +
[dc,dceq] = confungrad(x) | | |
The exitflag allows to know the status of the optimization which is given back by Ipopt. +
- exitflag=0 : Optimal Solution Found +
- exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal. +
- exitflag=2 : Maximum amount of CPU Time exceeded. Output may not be optimal. +
- exitflag=3 : Stop at Tiny Step. +
- exitflag=4 : Solved To Acceptable Level. +
- exitflag=5 : Converged to a point of local infeasibility.
For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/
+The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +
- output.Iterations: The number of iterations performed during the search +
- output.Cpu_Time: The total cpu-time spend during the search +
- output.Objective_Evaluation: The number of Objective Evaluations performed during the search +
- output.Dual_Infeasibility: The Dual Infeasiblity of the final soution
The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +
- lambda.lower: The Lagrange multipliers for the lower bound constraints. +
- lambda.upper: The Lagrange multipliers for the upper bound constraints. +
- lambda.eqlin: The Lagrange multipliers for the linear equality constraints. +
- lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints. +
- lambda.eqnonlin: The Lagrange multipliers for the non-linear equality constraints. +
- lambda.ineqnonlin: The Lagrange multipliers for the non-linear inequality constraints.
Examples
+function f1=gattainObjfun(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]; + +goal=[-5,-3,-2,-1,-4]; +weight=abs(goal) +gval = +[- 0.0000011 +- 63.999998 +- 2.0000002 +- 8. +3.485D-08] +z = +[4. 3.99] + +Run fgoalattain +[x,fval,attainfactor,exitflag,output,lambda]=fgoalattain(gattainObjfun,x0,goal,weight) | | |
Authors
+- Prajwala TM, Sheetal Shalini , 2015
+ + + + diff --git a/help/en_US/scilab_en_US_help/fminbnd.html b/help/en_US/scilab_en_US_help/fminbnd.html new file mode 100644 index 0000000..9b64d03 --- /dev/null +++ b/help/en_US/scilab_en_US_help/fminbnd.html @@ -0,0 +1,174 @@ + + +
+
fminbnd
+Solves a multi-variable optimization problem on a bounded interval
Calling Sequence
+xopt = fminbnd(f,x1,x2) +xopt = fminbnd(f,x1,x2,options) +[xopt,fopt] = fminbnd(.....) +[xopt,fopt,exitflag]= fminbnd(.....) +[xopt,fopt,exitflag,output]=fminbnd(.....) +[xopt,fopt,exitflag,output,lambda]=fminbnd(.....)
Parameters
+- f : +
a function, representing the objective function of the problem
+ - x1 : +
a vector, containing the lower bound of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables, where n is number of Variables
+ - x2 : +
a vector, containing the upper bound of the variables of size (1 X n) or (n X 1) or (0 X 0) where 'n' is the number of Variables. If x2 is empty it means upper bound is +infinity
+ - options : +
a list, containing the option for user to specify. See below for details.
+ - xopt : +
a vector of doubles, containing the the computed solution of the optimization problem.
+ - fopt : +
a scalar of double, containing the the function value at x.
+ - exitflag : +
a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.
+ - output : +
a structure, containing the information about the optimization. See below for details.
+ - lambda : +
a structure, containing the Lagrange multipliers of lower bound and upper bound at the optimized point. See below for details.
Description
+Search the minimum of a multi-variable function on bounded interval specified by : +Find the minimum of f(x) such that
+
The routine calls Ipopt for solving the Bounded Optimization problem, Ipopt is a library written in C++.
+The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +
- Syntax : options= list("MaxIter", [---], "CpuTime", [---], TolX, [----]); +
- MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take. +
- CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take. +
- TolX : a Scalar, containing the Tolerance value that the solver should take. +
- Default Values : options = list("MaxIter", [3000], "CpuTime", [600], TolX, [1e-4]);
The exitflag allows to know the status of the optimization which is given back by Ipopt. +
- exitflag=0 : Optimal Solution Found +
- exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal. +
- exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal. +
- exitflag=3 : Stop at Tiny Step. +
- exitflag=4 : Solved To Acceptable Level. +
- exitflag=5 : Converged to a point of local infeasibility.
For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/
+The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +
- output.Iterations: The number of iterations performed during the search +
- output.Cpu_Time: The total cpu-time spend during the search +
- output.Objective_Evaluation: The number of Objective Evaluations performed during the search +
- output.Dual_Infeasibility: The Dual Infeasiblity of the final soution
The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +
- lambda.lower: The Lagrange multipliers for the lower bound constraints. +
- lambda.upper: The Lagrange multipliers for the upper bound constraints.
Examples
+//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) | | |
Examples
+//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) | | |
Examples
+//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) | | |
Authors
+- R.Vidyadhar , Vignesh Kannan
+ + + + diff --git a/help/en_US/scilab_en_US_help/fmincon.html b/help/en_US/scilab_en_US_help/fmincon.html new file mode 100644 index 0000000..242c58b --- /dev/null +++ b/help/en_US/scilab_en_US_help/fmincon.html @@ -0,0 +1,302 @@ + + +
+
fmincon
+Solves a multi-variable constrainted optimization problem
Calling Sequence
+xopt = fmincon(f,x0,A,b) +xopt = fmincon(f,x0,A,b,Aeq,beq) +xopt = fmincon(f,x0,A,b,Aeq,beq,lb,ub) +xopt = fmincon(f,x0,A,b,Aeq,beq,lb,ub,nlc) +xopt = fmincon(f,x0,A,b,Aeq,beq,lb,ub,nlc,options) +[xopt,fopt] = fmincon(.....) +[xopt,fopt,exitflag]= fmincon(.....) +[xopt,fopt,exitflag,output]= fmincon(.....) +[xopt,fopt,exitflag,output,lambda]=fmincon(.....) +[xopt,fopt,exitflag,output,lambda,gradient]=fmincon(.....) +[xopt,fopt,exitflag,output,lambda,gradient,hessian]=fmincon(.....)
Parameters
+- f : +
a function, representing the objective function of the problem
+ - x0 : +
a vector of doubles, containing the starting values of variables of size (1 X n) or (n X 1) where 'n' is the number of Variables
+ - A : +
a matrix of doubles, containing the coefficients of linear inequality constraints of size (m X n) where 'm' is the number of linear inequality constraints
+ - b : +
a vector of doubles, related to 'A' and containing the the Right hand side equation of the linear inequality constraints of size (m X 1)
+ - Aeq : +
a matrix of doubles, containing the coefficients of linear equality constraints of size (m1 X n) where 'm1' is the number of linear equality constraints
+ - beq : +
a vector of doubles, related to 'Aeq' and containing the the Right hand side equation of the linear equality constraints of size (m1 X 1)
+ - lb : +
a vector of doubles, containing the lower bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables
+ - ub : +
a vector of doubles, containing the upper bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables
+ - nlc : +
a function, representing the Non-linear Constraints functions(both Equality and Inequality) of the problem. It is declared in such a way that non-linear inequality constraints are defined first as a single row vector (c), followed by non-linear equality constraints as another single row vector (ceq). Refer Example for definition of Constraint function.
+ - options : +
a list, containing the option for user to specify. See below for details.
+ - xopt : +
a vector of doubles, cointating the computed solution of the optimization problem
+ - fopt : +
a scalar of double, containing the the function value at x
+ - exitflag : +
a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.
+ - output : +
a structure, containing the information about the optimization. See below for details.
+ - lambda : +
a structure, containing the Lagrange multipliers of lower bound, upper bound and constraints at the optimized point. See below for details.
+ - gradient : +
a vector of doubles, containing the Objective's gradient of the solution.
+ - hessian : +
a matrix of doubles, containing the Lagrangian's hessian of the solution.
Description
+Search the minimum of a constrained optimization problem specified by : +Find the minimum of f(x) such that
+
The routine calls Ipopt for solving the Constrained Optimization problem, Ipopt is a library written in C++.
+The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +
- Syntax : options= list("MaxIter", [---], "CpuTime", [---], "GradObj", ---, "Hessian", ---, "GradCon", ---); +
- MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take. +
- CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take. +
- GradObj : a function, representing the gradient function of the Objective in Vector Form. +
- Hessian : a function, representing the hessian function of the Lagrange in Symmetric Matrix Form with Input parameters x, Objective factor and Lambda. Refer Example for definition of Lagrangian Hessian function. +
- GradCon : a function, representing the gradient of the Non-Linear Constraints (both Equality and Inequality) of the problem. It is declared in such a way that gradient of non-linear inequality constraints are defined first as a separate Matrix (cg of size m2 X n or as an empty), followed by gradient of non-linear equality constraints as a separate Matrix (ceqg of size m2 X n or as an empty) where m2 & m3 are number of non-linear inequality and equality constraints respectively. +
- Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);
The exitflag allows to know the status of the optimization which is given back by Ipopt. +
- exitflag=0 : Optimal Solution Found +
- exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal. +
- exitflag=2 : Maximum amount of CPU Time exceeded. Output may not be optimal. +
- exitflag=3 : Stop at Tiny Step. +
- exitflag=4 : Solved To Acceptable Level. +
- exitflag=5 : Converged to a point of local infeasibility.
For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/
+The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +
- output.Iterations: The number of iterations performed during the search +
- output.Cpu_Time: The total cpu-time spend during the search +
- output.Objective_Evaluation: The number of Objective Evaluations performed during the search +
- output.Dual_Infeasibility: The Dual Infeasiblity of the final soution
The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +
- lambda.lower: The Lagrange multipliers for the lower bound constraints. +
- lambda.upper: The Lagrange multipliers for the upper bound constraints. +
- lambda.eqlin: The Lagrange multipliers for the linear equality constraints. +
- lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints. +
- lambda.eqnonlin: The Lagrange multipliers for the non-linear equality constraints. +
- lambda.ineqnonlin: The Lagrange multipliers for the non-linear inequality constraints.
Examples
+//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) | | |
Examples
+//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) | | |
Examples
+//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) | | |
Examples
+//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) | | |
Authors
+- R.Vidyadhar , Vignesh Kannan
+ + + + diff --git a/help/en_US/scilab_en_US_help/fminunc.html b/help/en_US/scilab_en_US_help/fminunc.html new file mode 100644 index 0000000..97ffdbf --- /dev/null +++ b/help/en_US/scilab_en_US_help/fminunc.html @@ -0,0 +1,178 @@ + + +
+
fminunc
+Solves a multi-variable unconstrainted optimization problem
Calling Sequence
+xopt = fminunc(f,x0) +xopt = fminunc(f,x0,options) +[xopt,fopt] = fminunc(.....) +[xopt,fopt,exitflag]= fminunc(.....) +[xopt,fopt,exitflag,output]= fminunc(.....) +[xopt,fopt,exitflag,output,gradient]=fminunc(.....) +[xopt,fopt,exitflag,output,gradient,hessian]=fminunc(.....)
Parameters
+- f : +
a function, representing the objective function of the problem
+ - x0 : +
a vector of doubles, containing the starting of variables.
+ - options: +
a list, containing the option for user to specify. See below for details.
+ - xopt : +
a vector of doubles, the computed solution of the optimization problem.
+ - fopt : +
a scalar of double, the function value at x.
+ - exitflag : +
a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.
+ - output : +
a structure, containing the information about the optimization. See below for details.
+ - gradient : +
a vector of doubles, containing the the gradient of the solution.
+ - hessian : +
a matrix of doubles, containing the the hessian of the solution.
Description
+Search the minimum of an unconstrained optimization problem specified by : +Find the minimum of f(x) such that
+
The routine calls Ipopt for solving the Un-constrained Optimization problem, Ipopt is a library written in C++.
+The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +
- Syntax : options= list("MaxIter", [---], "CpuTime", [---], "Gradient", ---, "Hessian", ---); +
- MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take. +
- CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take. +
- Gradient : a function, representing the gradient function of the Objective in Vector Form. +
- Hessian : a function, representing the hessian function of the Objective in Symmetric Matrix Form. +
- Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);
The exitflag allows to know the status of the optimization which is given back by Ipopt. +
- exitflag=0 : Optimal Solution Found +
- exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal. +
- exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal. +
- exitflag=3 : Stop at Tiny Step. +
- exitflag=4 : Solved To Acceptable Level. +
- exitflag=5 : Converged to a point of local infeasibility.
For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/
+The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +
- output.Iterations: The number of iterations performed during the search +
- output.Cpu_Time: The total cpu-time spend during the search +
- output.Objective_Evaluation: The number of Objective Evaluations performed during the search +
- output.Dual_Infeasibility: The Dual Infeasiblity of the final soution
Examples
+//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) | | |
Examples
+//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) | | |
Examples
+//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) | | |
Authors
+- R.Vidyadhar , Vignesh Kannan
+ + + + diff --git a/help/en_US/scilab_en_US_help/index.html b/help/en_US/scilab_en_US_help/index.html index 03ce98c..fc07de0 100644 --- a/help/en_US/scilab_en_US_help/index.html +++ b/help/en_US/scilab_en_US_help/index.html @@ -32,7 +32,37 @@
- Symphony Toolbox
-
- lsqlin — Solves a linear quadratic problem. +
- fgoalattain — Solves a multiobjective goal attainment problem + + + + + +
- fminbnd — Solves a multi-variable optimization problem on a bounded interval + + + + + +
- fmincon — Solves a multi-variable constrainted optimization problem + + + + + +
- fminunc — Solves a multi-variable unconstrainted optimization problem + + + + + +
- linprog — Solves a linear programming problem. + + + + + +
- lsqlin — Solves a linear quadratic problem. diff --git a/help/en_US/scilab_en_US_help/jhelpmap.jhm b/help/en_US/scilab_en_US_help/jhelpmap.jhm index 0226c5e..be43c6e 100644 --- a/help/en_US/scilab_en_US_help/jhelpmap.jhm +++ b/help/en_US/scilab_en_US_help/jhelpmap.jhm @@ -3,6 +3,11 @@