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This topic has been discussed at some length on Cross Validated (aka stats.stackexchange) and Reddit: Why is Newton's method not widely used in machine learning? (see in particular Nick Alger's answer) Why use gradient descent with neural networks? L-BFGS and neural nets Why second order SGD convergence methods are unpopular for deep learning? How does the ...

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Yes, you are optimizing a knapsack problem. The objects, or "items" in most knapsack problem (KP) definitions, in your case is a set $S=\{s_{00}, s_{01}, ..,s_{0n}, s_{10}, .. s_{kn}\}$, which contains composite keyword-bid pairs, so $s_{ij}$ denotes an object labeled "keyword $i$ bid $j$". The reason you should think of your items as composite this way ...

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You should use a modeling language so that your code is independent of the underlying solver. cvxpy is a good choice. When I rewrite your model in cvxpy: #!/usr/bin/env python3 import cvxpy as cp import numpy as np from numpy.random import normal as randn Sample = 10 H = randn(size=(4,2,Sample))+1j*randn(size=(4,2,Sample)) h = randn(size=(4,1))+1j*randn(...

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