Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the propos...
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Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.
In this note we apply a lemma due to Sabach and Shtern to compute linear rates of asymptotic regularity for Halpern-type nonlinear iterations studied in optimization and nonlinear analysis.
In this note we apply a lemma due to Sabach and Shtern to compute linear rates of asymptotic regularity for Halpern-type nonlinear iterations studied in optimization and nonlinear analysis.
. In this paper, we first present several characterizations for the weak sharpness of the solution set of variational inequality problems on Hadamard manifolds. Some of these results answer an open question raised in ...
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. In this paper, we first present several characterizations for the weak sharpness of the solution set of variational inequality problems on Hadamard manifolds. Some of these results answer an open question raised in [L. V. Nguyen, Optimization, 70 (2021) 1443-1458]. We then establish some abstract results on the finite termination property for sequences generated by some iterative methods under the weak sharpness or linear conditioning of solution sets. Finally, finite convergence results for sequences generated by the proximal point algorithm for solving pseudomonotone variational inequalities are presented. Examples are also given to illustrate our results.
In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximalpoint iterative algorithm wi...
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In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximalpoint iterative algorithm with Bregman divergence is proposed and some strong convergence results for the proposed scheme under standard assumptions are obtained. Meanwhile, the convex optimization problems and the critical point problems are studied in the applications, and the recovery of the sparse signal is simulated in the numerical experiments.
作者：
He, XinXihua Univ
Sch Sci Chengdu 610039 Sichuan Peoples R China
In this paper, we introduce two accelerated primal-dual methods tailored to address linearly constrained composite convex optimization problems, where the objective function is expressed as the sum of a possibly nondi...
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In this paper, we introduce two accelerated primal-dual methods tailored to address linearly constrained composite convex optimization problems, where the objective function is expressed as the sum of a possibly nondifferentiable function and a differentiable function with Lipschitz continuous gradient. The first method is the accelerated linearized augmented Lagrangian method (ALALM), which permits linearization to the differentiable function;the second method is the accelerated linearized proximal point algorithm (ALPPA), which enables linearization of both the differentiable function and the augmented term. By incorporating adaptive parameters, we demonstrate that ALALM achieves the O(1/k(2)) convergence rate and the linear convergence rate under the assumption of convexity and strong convexity, respectively. Additionally, we establish that ALPPA enjoys the O(1/k) convergence rate in convex case and the O(1/k(2)) convergence rate in strongly convex case. We provide numerical results to validate the effectiveness of the proposed methods.
This paper aims to introduce a novel self-adaptive explicit iterative algorithm for solving the split common solution problem with monotone operator equations in real Hilbert spaces. This new approach does not employ ...
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This paper aims to introduce a novel self-adaptive explicit iterative algorithm for solving the split common solution problem with monotone operator equations in real Hilbert spaces. This new approach does not employ resolvent operators nor does it use the norms of the bounded linear operators (transfer mappings) from the source space to the image spaces.
In this paper, we extend the results for approximation semigroups for general resolvent maps including various resolvents of maps on a general convex geodesic metric space. For our study, we introduce the notion of (g...
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In this paper, we extend the results for approximation semigroups for general resolvent maps including various resolvents of maps on a general convex geodesic metric space. For our study, we introduce the notion of (general) resolvent maps which is a generalization of the resolvent maps in Lawson (J Lie Theory 33, 361-376, 2023) and then we prove several useful properties for the resolvent map and construct the approximation semigroups for resolvent maps. We also study the convergence of a proximalpoint like algorithm for the general resolvent map.
The Fantope-constrained sparse principal subspace estimation problem is initially proposed Vu et al. (Vu et al., 2013). This paper investigates a semismooth Newton based proximalpoint (P PASSN ) algorithm for solving...
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The Fantope-constrained sparse principal subspace estimation problem is initially proposed Vu et al. (Vu et al., 2013). This paper investigates a semismooth Newton based proximalpoint (P PASSN ) algorithm for solving the equivalent form of this problem, where a semismooth Newton (S SN ) method is utilized to optimize the inner problems involved in the P PASSN algorithm. Under standard conditions, the P PASSN algorithm is proven to achieve global convergence and asymptotic superlinear convergence rate. Computationally, we derive nontrivial expressions the Fantope projection and its generalized Jacobian, which are key ingredients for the P PASSN algorithm. Some numerical results on synthetic and real data sets are presented to illustrate the effectiveness of the proposed P PASSN algorithm for large-scale problems and superiority over the alternating direction method of multipliers (ADMM).
For minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in an Euclidean space we propose a stochastic incremental mirror descent algorithm constructed ...
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For minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in an Euclidean space we propose a stochastic incremental mirror descent algorithm constructed by means of the Nesterov smoothing. Further, we modify the algorithm in order to minimize over a nonempty closed convex set in an Euclidean space a sum of finitely many proper, convex and lower semicontinuous functions composed with linear operators. Next, a stochastic incremental mirror descent Bregman-proximal scheme with Nesterov smoothing is proposed in order to minimize over a nonempty closed convex set in an Euclidean space a sum of finitely many proper, convex and lower semicontinuous functions and a prox-friendly proper, convex and lower semicontinuous function. Different to the previous contributions from the literature on mirror descent methods for minimizing sums of functions, we do not require these to be (Lipschitz) continuous or differentiable. Applications in Logistics, Tomography and Machine Learning modelled as optimization problems illustrate the theoretical achievements
We introduce three new inertial shrinking projection algorithms with multiple inertial effects for solving split common solution problems with multiple output sets. We establish the convergence of the sequences genera...
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We introduce three new inertial shrinking projection algorithms with multiple inertial effects for solving split common solution problems with multiple output sets. We establish the convergence of the sequences generated by our proposed algorithms under some mild conditions on the control parameters. More precisely, we only require the boundedness of the coefficients of the inertial components. Moreover, our algorithms do not depend on the norms of the transfer mappings.
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