The constraints include both linear constraints and nonlinear constraints. The essential issue lies in to how to deal with the nonlinear constraints.
It would be better if this algorithm can transform these nonlinear constraints into the equivalent linear ones.
Hi, as your nonlinear constraints are nonconvex, your problem is nonconvex. Thus, you have to solve a general constrained problem. SQP methods or interrior-point methods are classical for this kind of problem. You can use fmincon (MATLAB) or any open-source code for this purpose.
Dear Nolberto Munier ,
I want to do that. But I don't know the principle and procedure.
Dear Yuan,
Can you provid us with the shape of your nonlinear constrains?
At matter fact, i also have a non convex MIQCP problem to solve, i am wondering if there is a way to convexify the problem? i only have a Cplex license and i think that he can only deal with convex MIQCP.
Liming: don't you have a senior scientist near-by? It would be so much easier if she could provide you with geometric insights into this question.
The nonlinear constraints can be linearized using the approach mentioned in the following articles:
1) http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200010
2) https://web.stanford.edu/class/msande312/restricted/Nonlin1.pdf
3) https://nptel.ac.in/courses/101108047/module7/Lecture%2016.pdf
4) https://x-engineer.org/undergraduate-engineering/advanced-mathematics/calculus-i/linearization-linear-approximation-nonlinear-function/
Hope it will help you.
Genetic Algorithm can be an alternative solution :
https://www.sciencedirect.com/science/article/abs/pii/S0096300307009861
http://rosario.toscano.free.fr/INS_HKA_R4.pdf
Dear Liming
I don't know which your problem is, but some time ago I solved a simple problem with two criteria and three non-linear constraints, by piece-wise each of the curves in three lineal sections.
Dear Liming Yuan I suggest that you linearize the model. You can consider the following methods (whichever works best) depending on the non linear constraint(s): (a) enumeration method; (b) discretization method; (c) dynamic programming method; (d) tailored method; and (e) second order cone programming method.
Such conditions are frequently occurred in nonlinear optimal control problems. It might be an efficient way to iteratively linearize the nonlinear constraints, namely the quasilinearization or successive convexification technique.
The following paper may be helpful
Article Stabilizing constrained chaotic system using a symplectic ps...
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