An Inertial Tseng's Type Proximal Algorithm for Nonsmooth and Nonconvex Optimization Problems
نویسندگان
چکیده
We investigate the convergence of a forward-backward-forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth function with a smooth one in the absence of convexity. The convergence is obtained provided an appropriate regularization of the objective satisfies the KurdykaLojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions.
منابع مشابه
Benson's algorithm for nonconvex multiobjective problems via nonsmooth Wolfe duality
In this paper, we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints. We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions. We also fo...
متن کاملInertial proximal alternating minimization for nonconvex and nonsmooth problems
In this paper, we study the minimization problem of the type [Formula: see text], where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the convergence by constructing a key function H that guarantees a sufficient decrease property of the iterates. In fact, we prove...
متن کاملAccelerated Proximal Gradient Methods for Nonconvex Programming
Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a...
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 کاملScalable nonconvex inexact proximal splitting
We study a class of large-scale, nonsmooth, and nonconvex optimization problems. In particular, we focus on nonconvex problems with composite objectives. This class includes the extensively studied class of convex composite objective problems as a subclass. To solve composite nonconvex problems we introduce a powerful new framework based on asymptotically nonvanishing errors, avoiding the commo...
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:
- J. Optimization Theory and Applications
دوره 171 شماره
صفحات -
تاریخ انتشار 2016