Originally posted by: hugh_medal

Hello,

I am trying to solve a separable nonlinear program (i.e., objective and constraints are sums of single-variable nonlinear functions f(x_j) j=1,..,n).

I am using a grid-point-approximation LP-formulation (i.e., form a piecewise-linear formulation of each nonlinear function using grid point variables http://see Sec. 11.3 of Bazarra et al., Nonlinear Programming, 3rd ed.).

In doing this, I need to ensure that at most two adjacent grid point variables are positive for each j. I have used SOS2 constraints to do this. However, that changes my LP into an IP.

Another option is to use a restricted basis rule, where I only allow a nonbasic variable to enter the basis if the new basis has no more than two adjacent grid point variables that are positive for each j.

My intuition is that the restricted basis rule method would be much faster than adding SOS2 constraints. Is my intuition correct?

I don't believe that I can implement the restricted basis rule in CPLEX. Do you know of any other LP-solver that would allow me to implement the restricted basis rule.

Thank you,
Hugh Medal
Ph.D. Candidate
Department of Industrial Engineering
University of Arkansas
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Originally posted by: SystemAdmin

CPLEX provides a full pivoting interface in the C layer. So, in principle you can implement any pricing rule that you want.

But are you sure that your problem can be solved by an LP algorithm? Or is the problem actually NP hard, and you need the tree search of the MIP engine?

Tobias
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Originally posted by: hugh_medal

The pivoting interface isn't available in the Java wrapper (ILOG Concert) is it?

The way I am interpreting the Bazarra book, as long as the objective function and constraint functions are separable function, my problem can be solved using the grid-point-approximation LP-formulation. Am I missing something?

Thanks for your help,
Hugh
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