arXiv subjects

Rong Hu

Publications and source records attributed to Rong Hu.

29 records · Page 2Linked to original sources

arXiv2022

Fast primal-dual algorithm via dynamical system for a linearly constrained convex optimization problem

By time discretization of a second-order primal-dual dynamical system with damping $α/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a linear equality constrained convex optimization problem. Under a suitable scaling condition, we show that the proposed algorithm enjoys a fast convergence rate for the objective residual and the feasibility violation, and the decay rate can reach $\mathcal{O}(1/k^{α-1})$ at the most. We also study convergence properties of the corresponding primal-dual dynamical system to better understand the acceleration scheme. Finally, we report numerical experiments to demonstrate the effectiveness of the proposed algorithm.

math.OC↗

arXiv2022

"Second-Order Primal'' + "First-Order Dual'' Dynamical Systems with Time Scaling for Linear Equality Constrained Convex Optimization Problems

Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical system with constant viscous damping and time scaling for the linear equality constrained convex optimization problem, which consists of a second-order ODE for the primal variable and a first-order ODE for the dual variable. When the scaling satisfies certain conditions, we prove its convergence property without assuming strong convexity. Even the convergence rate can become exponential when the scaling grows exponentially. We also show that the obtained convergence property of the dynamical system is preserved under a small perturbation.

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arXiv2022

SALIENCE: An Unsupervised User Adaptation Model for Multiple Wearable Sensors Based Human Activity Recognition

Unsupervised user adaptation aligns the feature distributions of the data from training users and the new user, so a well-trained wearable human activity recognition (WHAR) model can be well adapted to the new user. With the development of wearable sensors, multiple wearable sensors based WHAR is gaining more and more attention. In order to address the challenge that the transferabilities of different sensors are different, we propose SALIENCE (unsupervised user adaptation model for multiple wearable sensors based human activity recognition) model. It aligns the data of each sensor separately to achieve local alignment, while uniformly aligning the data of all sensors to ensure global alignment. In addition, an attention mechanism is proposed to focus the activity classifier of SALIENCE on the sensors with strong feature discrimination and well distribution alignment. Experiments are conducted on two public WHAR datasets, and the experimental results show that our model can yield a competitive performance.

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arXiv2021

Inertial primal-dual methods for linear equality constrained convex optimization problems

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an inexact inertial primal-dual method by linearizing the smooth individual function and solving the subproblem inexactly. Assuming merely convexity, we prove that the proposed methods enjoy $\mathcal{O}(1/k^2)$ convergence rate on the objective residual and the feasibility violation in the primal model. Numerical results are reported to demonstrate the validity of the proposed methods.

math.OC↗

arXiv2021

Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems

In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing the energy functions, we investigate the convergence rates with different choices of the damping coefficients and time scaling coefficients. Our results extend the inertial dynamical approaches for unconstrained convex optimization problems to affine constrained convex optimization problems.

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arXiv2021

A linesearch projection algorithm for solving equilibrium problems without monotonicity in Hilbert spaces

We propose a linesearch projection algorithm for solving non-monotone and non-Lipschitzian equilibrium problems in Hilbert spaces. It is proved that the sequence generated by the proposed algorithm converges strongly to a solution of the equilibrium problem under the assumption that the solution set of the associated Minty equilibrium problem is nonempty. Compared with existing methods, we do not employ Fejér monotonicity in the strategy of proving the convergence. This comes from projecting a fixed point instead of the current point onto a subset of the feasible set at each iteration. Moreover, employing an Armijo-linesearch without subgradient has a great advantage in CPU-time. Some numerical experiments demonstrate the efficiency and strength of the presented algorithm.

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arXiv2021

Solvability of a Regular Polynomial Vector Optimization Problem without Convexity

In this paper we consider the solvability of a non-convex regular polynomial vector optimization problem on a nonempty closed set. We introduce regularity conditions for the polynomial vector optimization problem and study properties and characterizations of the regularity conditions. Under the regularity conditions, we study nonemptiness and boundedness of the solution sets of the problem. As a consequence, we establish two Frank-Wolfe type theorems for the non-convex polynomial vector optimization problem. Finally, we investigate the solution stability of the non-convex regular polynomial vector optimization problem.

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arXiv2020

Asymptotic behavior of a nonautonomous evolution equation governed by a quasi-nonexpansive operator

We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by relying on Lyapunov analysis. Under a metric subregularity condition, we further derive a flexible global exponential-type rate for the distance of the trajectory to the set of fixed points. The results obtained are applied to analyze the asymptotic behavior of the trajectory of an adaptive Douglas-Rachford dynamical system, which is applied for finding a zero of the sum of two operators, one of which is strongly monotone while the other one is weakly monotone.

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arXiv2020

Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems

In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we investigate asymptotic properties of the proposed dynamical system as the time $t\to+\infty$. The convergence rates are derived for different choices of the damping coefficients. We also show that the obtained results are robust under external perturbations.

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arXiv2011

Extremely high energy cosmic ray as the probe of new physics

We explore the influence of new physics on extremely high energy cosmic ray (EXCER) particles. In particular, we devote our mind to one example of new physics, unparticle stuff, on one specific process that EXECRs participate in, photopion production of the EXECR nucleon with 2.7K cosmic microwave background radiation (CMBR). Through computing the differential cross section of virtual exchange of unparticle in the $p+γ\to p+ π^0$ process, we acquire the general consequence of new physics on the EXECR propagation. It is astonishing but reasonable that due to the lowness of interaction energy $\sqrt{s}$, the new physics will play a nearly negligible role in EXECR interaction.

astro-ph.HE↗

arXiv2009

Unparticle effects on cosmic ray photon and $e^\pm$

We study the effects of unparticle physics on the cosmic ray photon and $e^\pm$, including on the pair production (PP) and elastic scattering (ES) of cosmic ray photon off various background radiations, and on the inverse Compton scattering of cosmic ray $e^\pm$ with cosmic radiations. We compute the spin-averaged amplitudes squared of three processes and find that the advent of unparticle will never significantly change the interactions of cosmic ray photon and $e^\pm$ with various background radiations, although the available papers show that ES which occurs in the tree-level through unparticle exchanges will easily surpass PP in the approximate parameter regions.

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