Efficient method for solving globally optimal solutions of weighted LP norm and L2 norm optimization problems

This paper extends the existing L1 norm separable surrogate functional (SSF) iterative shrinkage algorithm to approximate the objective function of a weighted Lp norm and L2 norm optimization problem by N one dimensional independent objective functions. However, as the weighted Lp norm and L2 norm optimization problem is nonconvex, there may be more than one locally optimal solution. Hence, it is difficult to find the globally optimal solution. To address this difficulty, this paper further characterizes the regions that the signs of the convexity of the objective function within the regions remain unchanged. Then, the optimal solution within each region and eventually the globally optimal solution of the original optimization problem are found.