This is a class of problems called mixed integer programming, although that term is most commonly used in the OR/linear programming field. I think the term we use here is nonlinear integer programming.
http://en.wikipedia.org/wiki/Integer_programming http://arxiv.org/abs/0906.5171 I didn’t find anything relevant by searching the list of algorithms in NLopt. http://ab-initio.mit.edu/wiki/index.php/NLopt_Algorithms It’s possible that your problem can be recast into something usable. I am thinking about a complementarity type problem for which a global solver with constraints can be used since you have a 0/1 variable. Dale Smith, Ph.D. Senior Financial Quantitative Analyst Financial & Risk Management Solutions Fiserv Office: 678-375-5315 www.fiserv.com<http://www.fiserv.com/> From: NLopt-discuss [mailto:[email protected]] On Behalf Of Bj Wu Sent: Thursday, June 05, 2014 1:08 AM To: [email protected] Subject: [NLopt-discuss] nonlinear optimization with dummy variables Hi guys, I am new to nlopt. I have a nonlinear optimization problem like: object: Max{ Sum((1-(1-Pi*x1)*(1-Pi*x2)*(1-Pi*x3))*Ri) } (0<i<4 and Pi, Ri is constant) subject: x1+x2+x3 <= 2 xi is dummy variable which means it can only choose 0 or 1 value. Is there any API I can use to play with such dummy variables? For example, is it possible that I could use some API like the bounds setting APIs to fix the variables value to 0 or 1. Thank you very much. Best, Kevin
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