Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking … Read more

Projected subgradient minimization versus superiorization

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region is “simple … Read more

Superiorization: An optimization heuristic for medical physics

Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The superiorization methodology is presented as a heuristic solver for a … Read more

Perturbation resilience and superiorization of iterative algorithms

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the … Read more

On the Effectiveness of Projection Methods for Convex Feasibility

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of … Read more