# Conversion of "sine function to convex form

(HUSEYIN) #1

How can I convex the sine function in the objective function?

Your experience and information in this regard will be highly important to me.

With the hope of getting positive news from you,

Wishing you a wonderful day.

Best regards,

(Mark L. Stone) #2

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`, which is concave if `e` is positive, and convex if `e` is negative.However, it is doubtful either of those will work well in your optimization problem. A higher order Taylor series approximation for `sin(x)` will be neither convex nor concave.

Edit: Now I see you have an absolute value around the sin term. So only the one term Taylor series approximation could be used, unless a binary is introduced to handle the absolute value.

I recommend you use a non-convex nonlinear solver, which you can not do via CVX. You can consider using YALMIP. Why isn't CVX accepting my model? READ THIS FIRST!

(HUSEYIN) #3