A forward-backward dynamical approach to the minimization of the sum of a nonsmooth convex with a smooth nonconvex function
نویسندگان
چکیده
We address the minimization of the sum of a proper, convex and lower semicontinuous with a (possibly nonconvex) smooth function from the perspective of an implicit dynamical system of forward-backward type. The latter is formulated by means of the gradient of the smooth function and of the proximal point operator of the nonsmooth one. The trajectory generated by the dynamical system is proved to asymptotically converge to a critical point of the objective, provided a regularization of the latter satisfies the KurdykaLojasiewicz property. Convergence rates for the trajectory in terms of the Lojasiewicz exponent of the regularized objective function are also provided.
منابع مشابه
A block coordinate variable metric forward-backward algorithm
A number of recent works have emphasized the prominent role played by the KurdykaLojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of a non necessarily convex differentiable function and a non necessaril...
متن کاملSecond Order Forward-Backward Dynamical Systems For Monotone Inclusion Problems
We begin by considering second order dynamical systems of the from ẍ(t) + Γ(ẋ(t)) + λ(t)B(x(t)) = 0, where Γ : H → H is an elliptic bounded self-adjoint linear operator defined on a real Hilbert space H, B : H → H is a cocoercive operator and λ : [0,+∞)→ [0,+∞) is a relaxation function depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cau...
متن کاملA Primal-Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms
We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach, in the sense that the gradient and the linear operators involved are applied explici...
متن کاملAn inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the KurdykaLojasiewicz inequality, which is for i...
متن کاملLong term motion analysis for object level grouping and nonsmooth optimization methods = Langzeitanalyse von Bewegungen zur objektorientierten Gruppierung und nichglatte Optimierungsmethoden
This work deals with theoretical and practical aspects of convex and nonconvex optimization algorithms for several classes of problems. They are applied to several (low-level) computer vision tasks. The optical flow motion estimation problem, which is among them, is a potential source for improving motion based segmentation methods. The second, more practical part of this work focuses on such a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015