Convergence analysis of a variable metric forward–backward splitting algorithm with applications
نویسندگان
چکیده
منابع مشابه
On the Convergence of the Variable Metric Algorithm
The variable metric algorithm is a frequently used method for calculating the least value of a function of several variables. However it has been proved only that the method is successful if the objective function is quadratic, although in practice it treats many types of objective functions successfully. This paper extends the theory, for it proves that successful convergence is obtained provi...
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We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed.
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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...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2019
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2097-4