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Optimization problem with thousands of variables http://forum.alglib.net/viewtopic.php?f=2&t=4588 
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Author:  morfeus80 [ Wed Dec 06, 2023 2:44 pm ] 
Post subject:  Optimization problem with thousands of variables 
Hello everyone, I am trying to solve an optimization problem of a linear equation of the form F(x)=k1/x1+k2/x2+....+kn/xn, where "n" is of the order of 10k. The problem has about 10k nonlinear equality and nonlinear disequality constraints. To solve it I have used minnlc with SQP algorithm in C++, but the solution requires tenth of hours. Am I using a wrong solver that slows down everything or is this timing normal for the Alglib library? I saw the same problem to be solved in less than one minute, but I don't know which library had been used. 
Author:  Sergey.Bochkanov [ Thu Dec 07, 2023 4:38 pm ] 
Post subject:  Re: Optimization problem with thousands of variables 
Hi! The reason is that SQP present in ALGLIB 4.0 is a dense BFGSbased SQP, which indeed takes too long on largescale problems. An upcoming ALGLIB release will feature a largescale SQP based on a LBFGS update, which has much better performance. I will send you a development snapshot in a minute! 
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