Ordering of Lagrange multipliers (Lambda) occurs in the same way as it is done for FMINCON. The active constraints listed at the end of the execution of FMINCON are numbers. Here is the ordering used for constraints in FMINCON:
linear equalities
nonlinear equalities
lower bounds
upper bounds
linear inequalities
nonlinear inequalities
A detailed explanation of this can be found at the Related Solution listed at the bottom of the page.
In case of FGOALATTAIN, certain constraints exist for objective functions, in terms of achieving the goal. Note the Optimization problem formulation:
min { LAMBDA : F(X)-WEIGHT.*LAMBDA<=GOAL }
X,LAMBDA
This indicates that some nonlinear constraints are being added on the objective function that is different from other nonlinear constraints c(x).
Now, the order of Lagrange multipliers (Lambda) are :
linear equalities
nonlinear equalities
lower bounds
upper bounds
linear inequalities
nonlinear inequalities
Exact goal achieved %% NOTE the additional list
The Lambda structure is obtained as one of the outputs from FGOALATTAIN using the following syntax:
[x,fval,attainfactor,exitflag,output,lambda] = fgoalattain(...
returns a structure 'lambda' whose fields contain the Lagrange multipliers at the solution 'x'.
Lambda has the following field(s):
lower: LB
upper: UB
eqlin: Aeq*X = Beq
eqnonlin: Ceq(X)=0
ineqlin: A*X <= B.
ineqnonlin: C(X)<=0
NOTE: Lambda does NOT have the fields for "Exact goal achieved ".
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