Search results for "Proximal algorithm"
showing 4 items of 4 documents
Convergence of inertial prox-penalization and inertial forward-backward algorithms for solving bilevel monotone equilibrium problems
2023
The main focus of this paper is on bilevel optimization on Hilbert spaces involving two monotone equilibrium bifunctions. We present a new achievement consisting on the introduction of inertial methods for solving this type of problems. Indeed, two several inertial type methods are suggested: a proximal algorithm and a forwardbackward one. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the both iterative methods are established. Two particular cases illustrating the proposed methods are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under a sa…
Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems
2022
In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the iterative method are established. Two particular cases illustrating the proposed method are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under saddle point constraint. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. The algorithm and its convergence results improve and develop previous results i…
Higher-order Nonnegative CANDECOMP/PARAFAC Tensor Decomposition Using Proximal Algorithm
2019
Tensor decomposition is a powerful tool for analyzing multiway data. Nowadays, with the fast development of multisensor technology, more and more data appear in higherorder (order > 4) and nonnegative form. However, the decomposition of higher-order nonnegative tensor suffers from poor convergence and low speed. In this study, we propose a new nonnegative CANDECOM/PARAFAC (NCP) model using proximal algorithm. The block principal pivoting method in alternating nonnegative least squares (ANLS) framework is employed to minimize the objective function. Our method can guarantee the convergence and accelerate the computation. The results of experiments on both synthetic and real data demonstrate …
Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme
2021
Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using l1-norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP w…