Level Constrained First Order Methods for Function Constrained Optimization

Understand

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function.

• The algorithm converts the original problem into a sequence of convex subproblems.
• Formulating those subproblems requires the evaluation of at most one gradient value of the original objective and constraint functions.
• Either exact or approximate subproblem solutions can be computed efficiently in many cases.