From f7c5cbc61d5b52c749824298cfa39a95db2d879c Mon Sep 17 00:00:00 2001 From: Harpreet Date: Fri, 29 Jan 2016 16:38:03 +0530 Subject: linprog general tests added --- help/en_US/scilab_en_US_help/fgoalattain.html | 94 +++++++++++++-------------- 1 file changed, 46 insertions(+), 48 deletions(-) (limited to 'help/en_US/scilab_en_US_help/fgoalattain.html') diff --git a/help/en_US/scilab_en_US_help/fgoalattain.html b/help/en_US/scilab_en_US_help/fgoalattain.html index 0f7fdc9..2981e47 100644 --- a/help/en_US/scilab_en_US_help/fgoalattain.html +++ b/help/en_US/scilab_en_US_help/fgoalattain.html @@ -12,11 +12,11 @@
- << Symphony Toolbox + << FOSSEE Optimization Toolbox - Symphony Toolbox + FOSSEE Optimization Toolbox @@ -29,7 +29,7 @@ - Symphony Toolbox >> Symphony Toolbox > fgoalattain + FOSSEE Optimization Toolbox >> FOSSEE Optimization Toolbox > fgoalattain

fgoalattain

@@ -37,51 +37,51 @@

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(...)
+ 
xopt = fgoalattain(fun,x0,goal,weight)
+xopt = fgoalattain(fun,x0,goal,weight,A,b)
+xopt = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq)
+xopt = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub)
+xopt = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon)
+xopt = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,options)
+[xopt,fval] = fgoalattain(...)
+[xopt,fval,attainfactor] = fgoalattain(...)
+[xopt,fval,attainfactor,exitflag] = fgoalattain(...)
+[xopt,fval,attainfactor,exitflag,output] = fgoalattain(...)
+[xopt,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.

+
x0 : +

a vector of double, contains initial guess of variables.

+
A : +

a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.

+
b : +

a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.

+
Aeq : +

a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.

+
beq : +

a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.

+
lb : +

a vector of double, contains lower bounds of the variables.

+
ub : +

a vector of double, contains upper bounds of the 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

+
xopt : +

a vector of double, the computed solution of the optimization problem.

+
fopt : +

a double, the value of the function 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

+
exitflag : +

The exit status. See below for details.

+
output : +

The structure consist of statistics about the optimization. See below for details.

+
lambda : +

The structure consist of the Lagrange multipliers at the solution of problem. See below for details.

Description

fgoalattain solves the goal attainment problem, which is one formulation for minimizing a multiobjective optimization problem. @@ -102,14 +102,14 @@ It should be defined as type "list" and contains the following field

  • 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.

    +

    By default, the gradient options for fminimax are turned off and and fmincon does the gradient opproximation of gattainObjfun. In case the GradObj option is off and GradConstr option is on, fminimax approximates gattainObjfun 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);
    This will let fminimax know that the exact gradient of the objective function is known, so that it can change the calling sequence to the objective function. Note that, fGrad should be mentioned in the form of N x n where n is the number of variables, N is the number of functions in objective function.

    The constraint function must have header : 

    [c, ceq] = confun(x)
    -where x is a n x 1 matrix of dominmaxUbles, c is a 1 x nni matrix of doubles and ceq is a 1 x nne matrix of doubles (nni : number of nonlinear inequality constraints, nne : number of nonlinear equality constraints). +where x is a n x 1 matrix of doubles, c is a 1 x nni matrix of doubles and ceq is a 1 x nne matrix of doubles (nni : number of nonlinear inequality constraints, nne : number of nonlinear equality constraints). On input, the variable x contains the current point and, on output, the variable c must contain the nonlinear inequality constraints and ceq must contain the nonlinear equality constraints.

    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.

    @@ -145,7 +145,7 @@ It has type "struct" and contains the following fields.

    Examples

    - 
    function f1=fun(x)
+   
    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
@@ -153,14 +153,12 @@ It has type "struct" and contains the following fields.
 f1(5)=x(1)+x(2)-8
 endfunction
 x0=[-1,1];
-
 goal=[-5,-3,-2,-1,-4];
 weight=abs(goal)
-//xopt  = [-0.0000011 -63.999998 -2.0000002 -8 3.485D-08]
-//fval  = [4 3.99]
-
+//gval  =[- 0.0000011 -63.999998 -2.0000002 -8 3.485D-08]
+//z  = [4 3.99]
 //Run fgoalattain
-[xopt,fval,attainfactor,exitflag,output,lambda]=fgoalattain(fun,x0,goal,weight)
    
+[x,fval,attainfactor,exitflag,output,lambda]=fgoalattain(gattainObjfun,x0,goal,weight)

    Authors

    • Prajwala TM, Sheetal Shalini , 2015
    @@ -171,11 +169,11 @@ It has type "struct" and contains the following fields.
    Report an issue
    - << Symphony Toolbox + << FOSSEE Optimization Toolbox - Symphony Toolbox + FOSSEE Optimization Toolbox -- cgit