相关论文: Weak and Strong Superiorization: Between Feasibili…

The superiorization methodology can be thought of as lying conceptually between feasibility-seeking and constrained minimization. It is not trying to solve the full-fledged constrained minimization problem composed from the modeling…

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…

We consider the superiorization methodology, which can be thought of as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full fledged constrained minimization problem; rather, the task is…

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…

The superiorization methodology is intended to work with input data of constrained minimization problems, i.e., a target function and a constraints set. However, it is based on an antipodal way of thinking to the thinking that leads…

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…

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…

The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…

The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained…

Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative…

The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic…

In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in a conlinear space. Similar results are proved for a weaker…

Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward…

We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization method (SM), where the iterates of an asymptotically convergent…

We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…

Recent advancements in large language models have sparked interest in their extraordinary and near-superhuman capabilities, leading researchers to explore methods for evaluating and optimizing these abilities, which is called…

The superiorization methodology (SM) is an optimization heuristic in which an iterative algorithm, which aims to solve a particular problem, is ``superiorized'' to promote solutions that are improved with respect to some secondary…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

Weak-to-strong generalization, where weakly supervised strong models outperform their weaker teachers, offers a promising approach to aligning superhuman models with human values. To deepen the understanding of this approach, we provide…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…