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 constraints and the chosen objective function. Rather, the task is to find a feasible point which is "superior" (in a well-defined manner) with respect to the objective function, to one returned by a feasibility-seeking only algorithm. We telegraphically review the superiorization methodology and where it stands today and propose a rigorous formulation of its, yet only partially resolved, guarantee problem. The real-world situation in an application field is commonly represented by constraints defined by the modeling process and the data, obtained from measurements or otherwise dictated by the model-user. The feasibility-seeking problem requires to find a point in the intersection of all constraints without using any objective function to aim at any specific feasible point. At the heart of the superiorization methodology lies the modeler desire to use an objective function, that is exogenous to the constraints, in order to seek a feasible solution that will have lower (not necessarily minimal) objective function value. This aim is less demanding than full-fledged constrained minimization but more demanding than plain feasibility-seeking. Putting emphasis on the need to satisfy the constraints, because they represent the real-world situation, one recognizes the "asymmetric roles of feasibility-seeking and objective function reduction", namely, that fulfilling the constraints is the main task while reduction of the exogenous objective function plays only a secondary role. There are two research directions in the superiorization methodology: Weak superiorization and strong superiorization.
翻译:高级化方法可被视为在概念上在寻求可行性和限制最小化之间说谎,它不是试图解决由模型限制和选定目标功能构成的全面限制最小化问题,而是在目标功能方面找到一个可行的点,即“超级”(以明确界定的方式),到“唯一可行性研究算法”返回的方法。我们通过电报审查优势化方法及其目前的状况,提出严格制定该方法,但只是部分解决,保障问题。一个应用领域的实际情况通常由建模过程和数据、从计量或由模型用户决定的数据所定义的制约所代表。可行性研究问题需要找到一个与所有制约因素交错的“超级”点,而无需利用任何客观功能在任何具体可行的点上达到目标。 高级化方法的核心在于模型人希望使用一种客观功能,而这种功能的外向性只是寻求一种更低(不一定最低限度)客观功能的可行解决办法。这个目的比完全的、更高级的、更高级的研究作用的难度要小得多,因为比简单的可行性衡量方法更需要一种更高的、更精确的削减任务要求。