Convergence analysis of the Gauss-Newton method for convex inclusion problems and convex composite optimization
Publication in refereed journal


摘要Using the convex process theory we study the convergence issues of the iterative sequences generated by the Gauss-Newton method for the convex inclusion problem defined by a cone C and a Fréchet differentiable function F (the derivative is denoted by F’ ). The restriction in our consideration is minimal and, even in the classical case (the initial point x_0 is assumed to satisfy the following two conditions: F’ is Lipschitz around x_0 and the convex process T_{x_0} , defined by T_{x_0} = F’ (x_0) ● −C, is surjective), our results are new in giving sufficient conditions (which are weaker than the known ones) ensuring the convergence of the iterative sequence with initial point x_0. When F is analytic, we study point estimate conditions similar to Smale's conditions for nonlinear analytic equations. The same study is also made for the so-called convex-composite optimization problem (with objective function given as the composite of a convex function with a Fréchet differentiable map).
著者Chong Li, Kung Fu Ng
期刊名稱Pure and Applied Functional Analysis
出版社Yokohama Publishers
頁次591 - 619
關鍵詞The Gauss-Newton method, convex process, convex composite optimization, the weak-Robinson condition, the weak-Smale condition, majorizing function, convergence criterion

上次更新時間 2020-06-08 於 09:54