Why is lambda as an output of fmincon empty?

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I am using fmincon to perform convex, non linear programming, constrained optimization. I don't have any non linear equality constraints. I have linear equality and inequality constraints and non linear inequality constraints. I just have a few questions.
1. What does it mean for fmincon solver to give out an empty lambda?
2. How to check for quality of solution obtained by fmincon?
3. How to obtain duality gap in fmincon?
Viswanath Hariharan
Viswanath Hariharan on 27 Jun 2018
options = optimoptions(@fmincon,'OutputFcn',@inexact_outfun,'Algorithm','interior-point','MaxIterations',1e6,'MaxFunctionEvaluations',1e6,'StepTolerance',1e-10 );
[x,fval,exitflag,output,lambda,grad,hessian] = fmincon(fun,tempx0,A,b,Aeq,beq,lb,ub,@(x)nonlconstraints(x,j),options);
>> output_val{4}
ans =
struct with fields:
iterations: 4
funcCount: 307
constrviolation: 0.1956
stepsize: 0.0055
algorithm: 'interior-point'
firstorderopt: 0
cgiterations: 0
message: 'fmincon stopped by the output or plot function.'

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Accepted Answer

Steve Grikschat
Steve Grikschat on 27 Jun 2018
Hi Viswanath,
The lambda output is empty since the algorithm was stopped prematurely by the OutputFcn.
When that happens, the lambda (the Lagrangian duals) may be in an inconsistent state, so they are not returned. If you let the optimization complete normally, you should get a structure of duals in the lambda output (assuming the problem is not infeasible or unbounded).

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