A method is provided for reconstructing an image of an object that includes image elements. The method includes accessing measurement data associated with the image elements, introducing an auxiliary variable to transform an original problem of reconstructing the image to a constrained optimization problem, and solving the constrained optimization problem using a method of multipliers to create a sequence of sub-problems and solve the sequence of sub-problems. Solving the sequence of sub-problems includes reconstructing the image by optimizing a first objective function. The first objective function is optimized by iteratively solving a nested sequence of approximate optimization problems. An inner loop iteratively optimizes a second objective function approximating the first objective function. An outer loop utilizes the solution of the second objective function to optimize the first objective function.