At any x, I have to solve the following subproblems
min_{t,d} t
subject to ∇ f_j(x)^Td+1/2d^T ∇ ^2f_j(x)d+g_j(x+d)-g_j(x)
Hi, you may try the COBYLA code that solves nonlinear programming problems with inequality constraints without using derivatives. The objective function and the constraints are approximated linearly. A Python version seems to be available under:
https://docs.scipy.org/doc/scipy/reference/optimize.minimize-cobyla.html#optimize-minimize-cobyla
For a Java version see the following link:
https://github.com/cureos/jcobyla
For information about the method see the document attached.
Best
MATLAB is the best, see e.g., https://au.mathworks.com/help/optim/ug/constrained-nonlinear-optimization-algorithms.html and https://ww2.mathworks.cn/matlabcentral/answers/123532-different-results-from-fmincon-with-nonlcon
Dear Muhammad, you are true MATLAB is efficient (fmincon function) but the problem needs to be differentiable and it is not the case for Abu's problem.
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