1. A method for reconstructing an image of an object, the image including image elements, said method comprising: using a computer to perform: 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, wherein the original problem comprises an objective function formulated at least in part based on measurement data and prior knowledge of the image representing the object, and wherein the auxiliary variable comprises an additional term that is not part of the original problem; solving the constrained optimization problem using a method of multipliers to create a sequence of sub-problems and solve the sequence of sub-problems, wherein solving the sequence of sub-problems comprises reconstructing the image by optimizing a first objective function, wherein the first objective function is optimized by iteratively solving a nested sequence of approximate optimization problems, and wherein an inner loop iteratively optimizes a second objective function approximating the first objective function, and an outer loop utilizes the solution of the second objective function to optimize the first objective function, and wherein solving the constrained optimization problem comprises updating the auxiliary variable.