# Optimization Problem: x_1(sin(x_1)) such that exp(x_1)-1>=0

• ver_mathstats
So basically what I need to do is to find the second derivative of ##x\sin(x)## and see if it is positive?f

#### ver_mathstats

Homework Statement
Determine if the problem is a convex optimization problem
Relevant Equations
x_1(sin(x_1)) such that exp(x_1)-1>=0
I know to solve this problem we need to see if x1sinx1 is convex and if the constraint is convex. I already know that x1sinx1 is not convex so the problem is not convex, but for proving that this function is not convex is where I am confused. But how do I go about showing this? I'm assuming I cannot use a hessian or the definition because both use two variables? So do I just find the second derivative and see if it is positive? Is that sufficient enough?

Homework Statement:: Determine if the problem is a convex optimization problem
Relevant Equations:: x_1(sin(x_1)) such that exp(x_1)-1>=0

I know to solve this problem we need to see if x1sinx1 is convex and if the constraint is convex. I already know that x1sinx1 is not convex so the problem is not convex, but for proving that this function is not convex is where I am confused. But how do I go about showing this? I'm assuming I cannot use a hessian or the definition because both use two variables? So do I just find the second derivative and see if it is positive? Is that sufficient enough?
I took a class in linear programming many years ago, but I don't recall that it touched on convex optimization. From this link, https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf, I dug up the basics of convex optimization.

Apparently, what you want to do is to minimize ##x\sin(x)## subject to the constraint ##e^x \ge 1##. I've omitted the subscripts on x here since they serve no useful purpose in your problem. Section 1.3 of the book I linked to describes convex optimization and defines what it means for a constraint to be convex.

ver_mathstats and WWGD
I took a class in linear programming many years ago, but I don't recall that it touched on convex optimization. From this link, https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf, I dug up the basics of convex optimization.

Apparently, what you want to do is to minimize ##x\sin(x)## subject to the constraint ##e^x \ge 1##. I've omitted the subscripts on x here since they serve no useful purpose in your problem. Section 1.3 of the book I linked to describes convex optimization and defines what it means for a constraint to be convex.
Thank you, I wasn't provided a textbook for this class so this is very helpful