Hi there,
In my studies I come up with this nonconvex optimization problem
argmin |Ax|\_2+lamda\*|x|\_1 subject to x'x=1
where cost function is nonsmooth but convex and the constrant in nonconvex.
I tries subgradient projection method for convex constraints but the global solution is not my desired solution.
My question is that I should solve this problem hurestically or there is a reliable method for this nonconvex optimization problem?



non convex optimization
You can have a look of these papers：
 1. Jonathan H. Manton, Optimization algorithms exploiting unitary constraints.
 2. Zaiwen Zai and Wotao Yin, A feasible method for optimization with orthogonality constraints.


Wish these studies can help you. 


