Convex Constraint on Sine Wave Simularity

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So lets say you have a vector X = [x1 x2 x3 ..... xn]

You want to optimize a cost function over X.

However you want to constrain the vector X to look like a sine wave. Say you can parameterize a sine wave using a vector θ. Ideally then, I would like to have X look like a sine wave that belongs to the family of sine waves that is enclosed by:

(θ - e) < X < (θ + e) where e is some error margin.

My question is then, is there someway to formulate a constraint that a vector "looks similar" to a give sine wave?