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I am using cvxpy to maximize a function f(x) given the constraints -1 <= x <= 1. Let's call the solution x0. Now, I define a region around the optimal value f(x0) and want to find another solution x that lies within the defined region and that is maximally different from x0.

The problem statement looks as follows:

constraints = [-1 <= x, x <= 1, f(x) >= f(x0) - eps, f(x) <= f(x0) + eps]

objective_to_maximize = f(x) + cvxpy.norm(x - x0)

However, the cvxpy.norm(x - x0) that is supposed to find a maximally different solution leads to a non-convex problem and therefore a DCP error.

Is there any way to formulate my intention in a disciplined convex way?

Thanks a lot!

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  • $\begingroup$ A tip: You can use MathJax to typeset your mathematical formulas. This will make the question much easier to read. $\endgroup$ Mar 11 at 10:11

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