[Coin-ipopt] Coding constraint with both linear and nonlinear groups in SIF

[Kevin Chen]

Hi,

I am trying to solve a non-linear programming problem with one of the constraints being a combination of linear and nonlinear group, it's something like, 

sum(p[i]*x[i]) + exp(sum(a[i]*x[i]^4+b[i]*x[i]^3))

Linear              nonlinear

I've tried various ways of representing it in the SIF format (I only have access to CUTEr), none of them seems to work correctly.  For example, on the "SIF Reference Report" from the CUTEr site, it mentioned that groups with linear combinations of previous groups may be specified, so I defined,

GROUPS
 XN OBJ                X1           -0.25          X2              -0.75
 XL CONLE1          X1           15.0           X2              40.0
 ......
 ......
 G  NONLIN 
 G  LINEAR           X1            0.25           X2              0.75
 DG COMBINED    NONLIN    1.0            LINEAR      1.0

And then defined the element type/users and group type/uses for the NONLIN group.  The program ran without error message, but solved the problem as if the NONLIN term is zero (namely, COMBINED = 1.0*LINEAR)

I understand that I could code everything in the nonlinear term as Elements, including the "exp" function, and then declare a trivial group with the linear terms and the non-linear element exp( ....) .  But then that means I need to write a long equation for sum(a[i]*x[i]^4+.....), as well as it derivative and Hessian in the element individual data card.  Whereas if I defined exp(...) as a group, with a[i]*x[i]^4, and b[i]*x[i]^3, being repetitive nonlinear elements, I only need to describe the derivative and Hessian for exp(.) in the nontrivial group individual data card and for a[i]*x[i]^4, and b[i]*x[i]^3 in the element individual data card (I suppose).  

Any comment would be really appreciated.

kevin