arXiv subjects

Zhuoqing Zheng

Publications and source records attributed to Zhuoqing Zheng.

3 recordsLinked to original sources

arXiv2026

An Accelerated Proximal Bundle Method with Momentum

Proximal bundle methods (PBM) are a powerful class of algorithms for convex optimization. Compared to gradient descent, PBM constructs more accurate surrogate models that incorporate gradients and function values from multiple past iterations, which leads to faster and more robust convergence. However, for smooth convex problems, PBM only achieves an O(1/k) convergence rate, which is inferior to the optimal O(1/k^2) rate. To bridge this gap, we propose an accelerated proximal bundle method (APBM) that integrates Nesterov's momentum into PBM. We prove that under standard assumptions, APBM achieves the optimal O(1/k^2) convergence rate. Numerical experiments demonstrate the effectiveness of the proposed APBM.

math.OC↗

arXiv2026

Bundle EXTRA for Decentralized Optimization

Decentralized primal-dual methods are widely used for solving decentralized optimization problems, but their updates often rely on the potentially crude first-order Taylor approximations of the objective functions, which can limit convergence speed. To overcome this, we replace the first-order Taylor approximation in the primal update of EXTRA, which can be interpreted as a primal-dual method, with a more accurate multi-cut bundle model, resulting in a fully decentralized bundle EXTRA method. The bundle model incorporates historical information to improve the approximation accuracy, potentially leading to faster convergence. Under mild assumptions, we show that a KKT residual converges to zero. Numerical experiments on decentralized least-squares problems demonstrate that, compared to EXTRA, the bundle EXTRA method converges faster and is more robust to step-size choices.

math.OC↗

arXiv2025

Primal-Dual Bundle Methods for Linear Equality-Constrained Problems

Dual ascent (DA) and the method of multipliers (MM) are fundamental methods for solving linear equality-constrained convex optimization problems, and their dual updates can be viewed as the minimization of a proximal linear surrogate function of the negative Lagrange dual and augmented Lagrange dual function, respectively. However, the proximal linear surrogate function may suffer from low approximation accuracy, which leads to slow convergence of DA and MM. To accelerate their convergence, we adapt the proximal bundle surrogate framework that can incorporate a list of more accurate surrogate functions, to both the primal and the dual updates of DA and MM, leading to a family of novel primal-dual bundle methods. Our methods generalize the primal-dual gradient method, DA, the linearized MM, and MM. Under standard assumptions that allow for a broad range of surrogate functions, we prove theoretical convergence guarantees for the proposed methods. Numerical experiments demonstrate that our methods converge not only faster, but also significantly more robust with respect to the parameters compared to the primal-dual gradient method, DA, the linearized MM, and MM.

math.OC↗