arXiv subjects

Liqian Qin

Publications and source records attributed to Liqian Qin.

4 recordsLinked to original sources

arXiv2026

A primal-dual splitting algorithm for monotone inclusions with applications

In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal-dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators and cocoercive terms, as well as a composite monotone operator involving the linear map. The algorithm combines forward evaluations for the cocoercive components with backward resolvent steps for the monotone operators and employs a dual update for the linear composition term. It generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration. We prove weak convergence of the iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, we establish strong convergence under a mild regularity condition, such as uniform monotonicity. Numerical experiments on image deblurring and denoising problems demonstrate the efficiency and flexibility of the proposed algorithm.

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arXiv2025

Nonlinear three-operator splitting algorithms with momentum for monotone inclusions

In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each proposed method extends one of the classical schemes: the semi-forward-reflected-backward splitting algorithm, the semi-reflected-forward-backward splitting algorithm, and the outer reflected forward-backward splitting algorithm by incorporating a nonlinear momentum term. Under appropriate step-size conditions, we establish the weak convergence of all three algorithms, and further prove their $R$-linear convergence rates under strong monotonicity assumptions. Preliminary numerical experiments on both synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithms.

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arXiv2025

Nonlinear forward-backward-half forward splitting with momentum for monotone inclusions

In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method augments the forward-backward-half forward splitting algorithm with a nonlinear momentum term. Under appropriate conditions on the step-size, we prove the weak convergence of the proposed algorithm. A linear convergence rate is also obtained under the strong monotonicity assumption. Furthermore, we investigate a stochastic variance-reduced forward-backward-half forward splitting algorithm with momentum for solving finite-sum monotone inclusion problems. Weak almost sure convergence and linear convergence are also established under standard condition. Preliminary numerical experiments on synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithm.

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arXiv2025

Stochastic forward-backward-half forward splitting algorithm with variance reduction

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator and a cocoercive operator in a separable real Hilbert space. By deffining a Lyapunov function, we establish the weak almost sure convergence of the proposed algorithm, and obtain the linear convergence when one of the maximally monotone operators is strongly monotone. Numerical examples are provided to show the performance of the proposed algorithm.

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