The eigenvalue complementarity problem (EiCP) is a kind of very useful model, which is widely used in the study of many problems in mechanics, engineering, and economics. The EiCP was shown to be equivalent to a special nonlinear complementarity problem or a mathematical programming problem with complementarity constraints. The existing methods for solving the EiCP are all nonsmooth methods, in...

The aim of this paper is to construct Levenberg-Marquardt level set methods for inverse obstacle problems, and to discuss their numerical realization. Based on a recently developed framework for the construction of level set methods, we can define LevenbergMarquardt level set methods in a general way by varying the function space used for the normal velocity. In the typical case of a PDE-constr...

Google Earth Engine (GEE) has been widely used to process geospatial data in recent years. Although the current GEE platform includes functions for fitting linear regression models, it does not have function fit nonlinear limiting platform’s capacity and application. To circumvent this limitation, work proposes a general adaptation of Levenberg–Marquardt (LM) method models parallel processing f...

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the KurdykaLojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward met...

We proposed an intensity-based morphological pyramid image registration algorithm. This approach utilizes the global affine transformation model, also considering radiometric changes between images. With the morphological pyramid structure, Levenberg-Marquardt optimization, and bilinear interpolation, this algorithm can be implemented hierarchically and iteratively with capability of measuring,...

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the KurdykaLojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward met...