Lagrange multiplier values after solving problem with Interior point method (using IPOPT solver)

[Tejaswini Darure]

Hello, 

I am solving an nonlinear optimization problem using IPOPT solver. 

>>sdpvar x(4)

>>constraints = [ 25-x(1)*x(2)*x(3)*x(4) <= 0];

>>constraints=[constraints;sum(x(1:4).^2)-40 == 0];

>>constraints=[constraints;1<=x(1:4)<=5];

>>objective = x(1)*x(4)*(x(1)+x(2)+x(3))+x(3) ;

>>options = sdpsettings('solver','ipopt','sdpa.maxIteration',100,'verbose',1,'usex0',[1,5,5,1]) ;

>>optimize(constraints,objective,options);

>>value(objective)

I need to access values of Lagrange multiplers also. 

How can I do that? 

Thanks a ton in advance. 

Regards,

[Johan Löfberg]

YALMIP does not deal with duals on nonlinear programs.

The best you can do is to turn on the option 'savesolveroutpu't, and the look at the solveroutput returned in the output from optimize, and see if that nonlinear solver has returned any dual information (the field info would be the only possibility in ipopt)

[Tejaswini Darure]

Thank you Johan for quick reply. 

[Mark L. Stone]

Or if you have to, compute the Jacobian (matrix of gradients) of the active (satisfied with equality) constraints.  Then formulate and solve the non-negatively constrained (for active <= constraints) linear least squares problem, which is a convex QP, to determine the Lagrange multipliers of the active constraints.  The Lagrange multipliers of inactive constraints are all equal to zero.

[Tejaswini Darure]

Thank you Mark!