# Conversion of “sine function to convex form

The sine function is non-concave and non-convex, which is difficult to handle.

I would like to ask whether the sine function can adopt the first-order Taylor expansion, sin(x)=sin(xl)+cos(xl)(x-xl) with the xl is the feasible point in the l-th iteration.

Since the sine function rarely appears in optimization, I don’t know whether it’s reasonable to do so

I am a student who is new to optimization. I hope someone can put forward their valuable suggestions and ideas.

The same answer I gave in the other thread you posted in:

Trigonometric functions are neither convex nor concave,. They can only be “convexified” by means of an approximation, such as a suitable Taylor series. The one term Taylor series approximation for sin(x) is x, and the two term Taylor series approximation is x - x^3/6, is convex for x < 0 and concave for x > 0, hence neither convex nor concave…Any higher order Taylor series approximation for sin(x) will be neither convex nor concave. `cos(x)` does allow the Taylor series approximation `1-x^2/2`, which is concave, and may or may not be adequate for purposes of optimization.

I recommend you use a non-convex nonlinear solver, which you can not do via CVX. You can consider using YALMIP…

Thank you for your reply. The result is very strange when using CVX to solve the problem. I will try more by myself, thank you again for your answer