In this paper, we develop a parameterized proximal point algorithm (PPPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case O(1/t) convergence rate, where t denotes the iteration number. By properly choosing the algorithm parameters, numerical experiments on solvin...

We propose a generalized proximal point algorithm (PPA), in the generic setting of finding a root of a maximal monotone operator. In addition to the classical PPA, a number of benchmark operator splitting methods in the PDE and optimization literatures can be retrieved by this generalized PPA scheme. We establish the convergence rate of this generalized PPA scheme under different conditions, in...

Based on a notion of relatively maximal m -relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar’s theorem 1976 on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this newmodel, is simpler and compact than that of the celebrated technique of R...

We present several strong convergence results for the modified proximal point algorithm xn+1 = αnu + (1 − αn)Jβnxn + en (n = 0, 1, . . .; u, x0 ∈ H given, and Jβn = (I + βnA) −1, for a maximal monotone operator A) in a real Hilbert space, under new sets of conditions on αn ∈ (0, 1) and βn ∈ (0,∞). These conditions are weaker than those known to us and our results extend and improve some recent ...

The problem of the minimization of least squares functionals with l penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are only a few of them which come with a proper convergence analysis in the infinite dimensional setting. In this work we provide an algorithm from a class which have not...

It is known that the proximal point algorithm converges weakly to a zero of a maximal monotone operator, but it fails to converge strongly. Then, in (Math. Program. 87:189-202, 2000), Solodov and Svaiter introduced the new proximal-type algorithm to generate a strongly convergent sequence and established a convergence property for the algorithm in Hilbert spaces. Further, Kamimura and Takahashi...

In this paper we consider the contraction-proximal point algorithm: xn+1 = αnu+λnxn+γnJβnxn, where Jβn denotes the resolvent of a monotone operator A. Under the assumption that limn αn = 0, ∑ n αn = ∞, lim infn βn > 0, and lim infn γn > 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosa...

This paper proposes a proximal iteratively reweighted algorithm to recover a low-rank matrix based on the weighted fixed point method. The weighted singular value thresholding problem gains a closed form solution because of the special properties of nonconvex surrogate functions. Besides, this study also has shown that the proximal iteratively reweighted algorithm lessens the objective function...