Proximal Gradient Method (PGM) for a Function Model with More than 2 Functions (Sum of Functions)

1. Is proximal gradient a descent method?
2. What is proximal point algorithm?
3. What does a proximal operator do?
4. What is projected gradient descent?

Is proximal gradient a descent method?

Proximal Gradient Descent, like regular Gradient Descent, is a "descent" method where the objective value is guaranteed to decrease. In fact, the assumptions for Proximal Gradient Descent's are the identical to the Gradient Descent assumptions for .

What is proximal point algorithm?

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.

What does a proximal operator do?

The proximal operator transforms one function f(·) into another function proxf (·).

What is projected gradient descent?

▶ Projected Gradient Descent (PGD) is a standard (easy and simple) way to solve constrained optimization problem. ▶ Consider a constraint set Q ⊂ Rn, starting from a initial point x0 ∈ Q, PGD iterates the following equation until a stopping condition is met: xk+1 = PQ ( xk − αk∇f(xk) ) .