Description
Title: BADLY CONDITIONED INVERSE PARAMETRIC PROBLEMS IMPOSE MISFIT LANDFORMS
Abstract: In this article, we present a novel topological taxonomy that enables us to identify and classify various solutions to parametric inverse problems with ill-conditioned conditions that arise in engineering, geophysics, medicine, etc. The landforms of the misfit landscape, whether they are located around minima (lowlands), maxima (uplands), or stationary points, are distinguished by this taxonomy as areas of insensitivity to parameters (shelves). We have established that they meet the crucial separability and completeness conditions. There are no other positive measure subsets in the admissible domain on which the misfit function takes a constant value, and in particular, lowlands, uplands, and shelves are pairwise disjoint. The second taxonomy, the “local” one, which describes the different kinds of ill-conditioning in a given solution, is related to the topological one. In addition to selecting and profiling the complex optimization strategies used to solve these problems, we anticipate that the proposed results will be useful for a better and more precise formulation of ill-conditioned inverse problems.
Keywords: taxonomy of ill-conditioned problems, ill-posed global optimization problems, fitness landscapes
Paper Quality: SCOPUS / Web of Science Level Research Paper
Paper type: Analysis Based Research Paper
Subject: Computer Science
Writer Experience: 20+ Years
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