A Randomized Block Coordinate Iterative Regularized Gradient Method for High-dimensional Ill-posed Convex Optimization

Understand

Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level problem, a solution that minimizes a secondary metric.

• Our goal is to address the high-dimensionality of the bilevel problem, and the nondifferentiability of the objective function.
• Minimal norm gradient, sequential averaging, and iterative regularization are some of the recent schemes developed for addressing the bilevel problem.
• But none of them address the high-dimensional structure and nondifferentiability.