The generalized proximal point algorithm with step size 2 is not necessarily convergent
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DOI: 10.1007/s10589-018-9992-3
Abstract: The proximal point algorithm (PPA) is a fundamental method in optimization and it has been well studied in the literature. Recently a generalized version of the PPA with a step size in (0, 2) has been… read more here.
Keywords: step size; step; proximal point; point algorithm ... See more keywords
Strong Convergence of Two Proximal Point Algorithms with Possible Unbounded Error Sequences
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DOI: 10.1007/s10957-016-1028-5
Abstract: We consider a proximal point algorithm with errors for a maximal monotone operator in a real Hilbert space, previously studied by Boikanyo and Morosanu, where they assumed that the zero set of the operator is… read more here.
Keywords: error; proximal point; point; operator ... See more keywords
A Proximal Point Algorithm Revisited and Extended
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DOI: 10.1007/s10957-019-01536-5
Abstract: This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222–235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroşanu (Optim Lett 7:415–420, 2013) is discussed.… read more here.
Keywords: algorithm; algorithm revisited; point algorithm; proximal point ... See more keywords
Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications
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DOI: 10.1007/s11075-020-00945-2
Abstract: In this paper, we combine the S-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal., 8(1), 61–79 2007) with the proximal point algorithm introduced by Rockafellar (SIAM J. Control Optim., 14, 877–898 1976)… read more here.
Keywords: asymptotically quasi; nonexpansive mappings; proximal point; point ... See more keywords
The generalized contraction proximal point algorithm with square-summable errors
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DOI: 10.1007/s13370-016-0453-9
Abstract: Let $$(x_n)$$(xn) be a sequence generated by $$x_{n+1}=\alpha _nu+\gamma _nx_n+\delta _nJ_{\beta _n}x_n+e_n$$xn+1=αnu+γnxn+δnJβnxn+en for $$n\ge 0$$n≥0, where $$J_{\beta _n}$$Jβn is the resolvent of a maximal monotone operator A with $$\beta _n\in (0,\infty )$$βn∈(0,∞), $$u,x_0\in H$$u,x0∈H, $$(e_n)$$(en)… read more here.
Keywords: point algorithm; proximal point; beta; generalized contraction ... See more keywords
On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds
Sign Up to like & getrecommendations! Published in 2017 at "Journal of the Operations Research Society of China"
DOI: 10.1007/s40305-016-0129-z
Abstract: In this paper, we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions… read more here.
Keywords: point algorithm; hadamard manifolds; proximal point; point ... See more keywords
On the Convergence Rate of a Proximal Point Algorithm for Vector Function on Hadamard Manifolds
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DOI: 10.1007/s40305-016-0146-y
Abstract: The proximal point algorithm has many interesting applications, such as signal recovery, signal processing and others. In recent years, the proximal point method has been extended to Riemannian manifolds. The main advantages of these extensions… read more here.
Keywords: point; proximal point; vector function; point algorithm ... See more keywords
On the weak and strong convergence of the proximal point algorithm in reflexive Banach spaces
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DOI: 10.1080/02331934.2017.1337764
Abstract: Abstract In this paper, some proximal point algorithms (PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences generated by the PPAs with… read more here.
Keywords: strong convergence; proximal point; weak strong; banach spaces ... See more keywords
Complexity Certification of Proximal-Point Methods for Numerically Stable Quadratic Programming
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DOI: 10.1109/lcsys.2020.3038035
Abstract: When solving a quadratic program (QP), one can improve the numerical stability of any QP solver by performing proximal-point outer iterations, resulting in solving a sequence of better conditioned QPs. In this letter we present… read more here.
Keywords: proximal point; certification proximal; complexity certification; point ... See more keywords
A Linear Programming Method Based on Proximal-Point Iterations With Applications to Multi-Parametric Programming
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DOI: 10.1109/lcsys.2021.3138218
Abstract: We propose a linear programming method that is based on active-set changes and proximal-point iterations. The method solves a sequence of least-distance problems using a warm-started quadratic programming solver that can reuse internal matrix factorizations… read more here.
Keywords: method based; linear programming; proximal point; programming method ... See more keywords
A strongly convergent modification of the proximal point algorithm in nonsmooth Banach spaces
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DOI: 10.24193/fpt-ro.2018.1.09
Abstract: Rockafellar’s proximal point algorithm is known to be not strongly convergent in general in an infinite-dimensional Hilbert space. Effort has thus been made to modify this algorithm so that strong convergence is guaranteed. In this… read more here.
Keywords: strongly convergent; point algorithm; convergent modification; proximal point ... See more keywords