arXiv subjects

Xiaowei Pang

Publications and source records attributed to Xiaowei Pang.

4 recordsLinked to original sources

arXiv2025

Shape optimization problems with random coefficients via the penalty method

For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the diffusion coefficients and minimize objective functions in mean value form. Finite element method, Monte Carlo method and accelerated version of the gradient descent method are applied to solve the corresponding discretized problem. The convergence analysis and numerical results are included.

math.OC↗

arXiv2025

Joint Trajectory and Resource Optimization for HAPs-SAR Systems with Energy-Aware Constraints

This paper investigates the joint optimization of trajectory planning and resource allocation for a high-altitude platform stations synthetic aperture radar (HAPs-SAR) system. To support real-time sensing and conserve the limited energy budget of the HAPs, the proposed framework assumes that the acquired radar data are transmitted in real time to a ground base station for SAR image reconstruction. A dynamic trajectory model is developed, and the power consumption associated with radar sensing, data transmission, and circular flight is comprehensively analyzed. In addition, solar energy harvesting is considered to enhance system sustainability. An energy-aware mixed-integer nonlinear programming (MINLP) problem is formulated to maximize radar beam coverage while satisfying operational constraints. To solve this challenging problem, a sub-optimal successive convex approximation (SCA)-based framework is proposed, incorporating iterative optimization and finite search. Simulation results validate the convergence of the proposed algorithm and demonstrate its effectiveness in balancing SAR performance, communication reliability, and energy efficiency. A final SAR imaging simulation on a 9-target lattice scenario further confirms the practical feasibility of the proposed solution.

eess.SY↗

arXiv2025

A new iterated Tikhonov regularization method for Fredholm integral equation of first kind

We consider Fredholm integral equation of the first kind, present an efficient new iterated Tikhonov method to solve it. The new Tikhonov iteration method has been proved which can achieve the optimal order under a-priori assumption. In numerical experiments, the new iterated Tikhonov regularization method is compared with the classical iterated Tikhonov method, Landweber iteration method to solve the corresponding discrete problem, which indicates the validity and efficiency of the proposed method.

math.NA↗

arXiv2020

Gr\"obner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$

The author is mainly interest in the Gr\"{o}bner-Shirshov bases of finite Coxeter groups. It is known that the finite Coxeter groups are classified in terms of Coxeter-Dynkin diagrams. Under the fixed order, it is worth mention that the presentation of group determines the Gr\"{o}bner-Shirshov bases of group. In this paper, the author rearranges the generators, marks them on Coxeter-Dynkin diagrams, and gets a simple presentation of the Gr\"{o}bner-Shirshov bases for Coxeter groups of types $G_2, F_4, E_6$ and $E_7$. This article also gives the Gr\"{o}bner-Shirshov basis of Coxeter group of type $E_8$.

math.GR↗