A subgradient based convex approximations method for DC programming and its applications
We consider an optimization problem that minimizes a function of the form $f=f_0+f_1 f_2$ with the constraint $g h\leq 0$ where $f_0$ is continuous differentiable, $f_1,f_2$ are convex and $g,h$ are lower semicontinuous convex. We propose to solve the problem by an inexact subgradient based convex approximations method. Under mild assumptions, we show that the method is guaranteed to converge to a stationary point. Finally, some preliminary numerical results are given.