arXiv subjects

Mingming Xu

Publications and source records attributed to Mingming Xu.

11 recordsLinked to original sources

arXiv2026

Face Identification via Polyhedral Relaxations for Binary Programs: A Comparison with Factor-Width Partial Facial Reduction

Facial reduction (FR) is a preprocessing technique used to restore Slater's condition in semidefinite programming (SDP), but each step generally requires solving an auxiliary SDP. Factor-width-$k$ partial FR restricts the class of exposing matrices. Increasing $k$ enlarges this class, but, for $k\geq3$, the auxiliary problem remains an SDP involving positive semidefinite blocks of order $k$. For SDP relaxations of binary programs, we replace this auxiliary SDP by an LP-based face-identification method. We construct a polyhedron in subset-indexed moment variables that has polynomial size for fixed $k$. The resulting face contains every feasible binary lift and is contained in every face exposed by a factor-width-$k$ exposing matrix from the same auxiliary system. Thus, linear programming identifies a face no larger than those obtained from the factor-width-$k$ auxiliary SDP while preserving all feasible binary points. To iterate the construction, we represent each identified face by linear equations in the original matrix variable, thereby retaining the moment-matrix indexing and the factor-width comparison at every iteration.

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arXiv2026

A Primal Approach to Facial Reduction for SDP Relaxations of Combinatorial Optimization Problems

We propose a novel facial reduction algorithm tailored to semidefinite programming relaxations of combinatorial optimization problems with quadratic objective functions. Our method leverages the specific structure of these relaxations, particularly the availability of feasible solutions that can often be generated efficiently in practice. By incorporating such solutions into the facial reduction process, we substantially simplify the reduction steps. On average, our facial reduction algorithm is four times faster than the standard implementation on the considered benchmark sets, providing significantly improved preprocessing for SDP relaxations in combinatorial optimization.

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arXiv2026

Face Structure in Partial Facial Reduction of Semidefinite Relaxations of Binary Programs

Semidefinite relaxations of binary optimization problems often fail Slater's condition. Full facial reduction restores strict feasibility but may require auxiliary problems as costly as the original relaxation. We analyze partial facial reduction based on tractable inner approximations of the positive semidefinite cone: the nonnegative diagonal, diagonally dominant (DD), and scaled diagonally dominant (SDD) cones. For this class of SDP relaxations, we prove that every terminal face identified by SDD-partial FR is described by variables fixed to zero or one and groups of variables forced to be equal. The face admits a full-column-rank $\{0,1\}$ basis matrix with disjoint column supports, yielding a natural reduced formulation that can preserve sparsity. For polyhedral inner approximations, we characterize the face exposed at each step through the inequalities active on the associated outer relaxation. We also establish sharp limitations. We construct a family with singularity degree two for which DD- and SDD-partial FR require the maximum possible number of steps. We further show that factor-width restrictions can prevent detection of dense valid affine equalities. These results characterize both the structure recovered by tractable partial FR and the cost of restricting the exposing-matrix search.

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arXiv2026

SDP Approach to Quadratic Vertex-Disjoint Paths Problem

We study the quadratic $k$-vertex-disjoint paths problem (Q-$k$-VDP), which seeks $k$ vertex-disjoint paths in a directed graph that minimize a nonconvex quadratic objective function. We formulate the problem as a binary quadratic program and apply a systematic graph reduction to manage its dimensionality. To obtain a tractable bounding model, we drop the subtour-elimination constraints and derive a semidefinite programming (SDP) relaxation. We then solve this relaxed model within a branch-and-bound framework, where the bounds are computed from the SDP relaxation using a tailored alternating direction method of multipliers. Computational results show that our proposed method consistently outperforms Gurobi by solving more instances to optimality, especially on challenging large-scale instances.

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arXiv2026

Path to Diversity: A Primer on ISAC-izing Commodity Wi-Fi for Practical Deployments

Integrated Sensing and Communication (ISAC) has emerged as a key paradigm in next-generation wireless networks. While the ubiquity and low cost of commodity Wi-Fi make it an ideal platform for wide-scale sensing, it is the continuous evolution of Wi-Fi standards-towards higher frequency bands, wider bandwidths, and larger antenna arrays-that fundamentally unlocks the physical resources required for high-performance ISAC. To structure this rapidly expanding field, numerous surveys have appeared. However, prevailing literature predominantly adopts a top-down perspective, emphasizing upper-layer applications or deep learning models while treating the physical layer as an opaque abstraction. Consequently, these works often fail to touch the bottom layer of signal formation and lack technical guidance on overcoming the physical barriers that constrain sensing performance. To bridge this gap, this tutorial takes a bottom-up approach, systematically analyzing the sensing gains brought by Wi-Fi advancements through the lens of physical-layer diversity. We organize the framework around four orthogonal dimensions: i) Temporal Diversity addresses synchronization gaps to enable absolute ranging; ii) Frequency Diversity expands the effective bandwidth to sharpen range resolution; iii) Link Diversity leverages distributed topologies and digital feedback to achieve ubiquitous observability; and iv) Spatial Diversity utilizes multi-antenna arrays to combine passive angular discrimination with active directional control. Collectively, these orthogonal dimensions resolve fundamental ambiguities in time, range, and space, bridging physical capabilities with challenging sensing diversities. By synthesizing these dimensions, this tutorial provides a comprehensive guide for "ISAC-izing" commodity Wi-Fi, paving the way for future standardization and robust deployment.

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arXiv2025

CPI-C: Cool Planet Imaging Coronagraph on Chinese Space Station Survey Telescope

Cool Planet Imaging Coronagraph (CPI-C) on Chinese Space Station Survey Telescope (CSST) is proposed to direct image the cool planets around nearby solar-type stars (within 40 pc). The core scientific objective of CPI-C is to conduct high-contrast directly imaging surveys of exoplanets ranging in size from Neptune-like to Jupiter-like, located at separations of 0.5 to 5 AU from their host stars, and to perform systematic spectroscopic analysis of the detected planets through high-precision multi-band photometry. CPI-C employs a step-transmission apodization technique to suppress the diffraction noises from the telescope pupil and a precise phase correction technique to eliminate the speckle noises due to imperfections of the optical surfaces. The contrast requirement is better than $10^{-8}$ at an inner working angle (IWA) of $3-4\lambda/D$, in the visible wavelength from 600 nm to 900 nm. CPI-C will be the first space-based instrument capable of directly imaging the reflection light from the cool exoplanets in the visible wavelength enabling the measurement of key physical parameters such as the effective temperature, surface gravity, radius, mass, and other key parameters. The potential observation results will significantly contribute to further understand the formation and evolution mechanisms of planets, which will also lay a solid foundation for future confirmation of the Earth-twins in the next generation space flagship missions.

astro-ph.EP↗

arXiv2025

Thermal design of focal plane assembly of wavefront camera for exoplanet imaging corona module

The focal plane assembly of wavefront camera is the key imaging device of wavefront detection camera and the key load of the exoplanet imaging coronagraph module. In order to ensure the imaging quality and reduce the dark current and thermal noise, it is necessary to effectively dissipate the heat of the focal plane CCD and other high-power electronic devices to ensure the working performance and reliability of the focal plane assembly. Based on the limited space and cooling resources, this paper adopts the flexible graphene heat conducting cable and grooved heat pipes, and carries out detailed thermal design and thermal analysis of its cooling path. The finite element model is established by thermal analysis software and thermal simulation is carried out. in that steady state, the work temperature range of the CCD chip is -12.8 to -10.9 celsius, which meets the temperature control index, and the work temperatures of other components are also within the design requirements, which indicate that the thermal design scheme is reasonable and feasible, and meets the task requirements.

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arXiv2025

Design and dynamics experiment of filter wheel mechanism of space coronagraph

In order to realize multi-spectral imaging of space coronagraph, a compact filter wheel mechanism is designed. The filters with different spectral transmittance can be cut into the optical path at different times by this mechanism. Because the image contrast of space coronagraph is very high, the high stability requirement for the optical unit of coronagraph is put forward. Small modulus worm gear and worm are taken by the mechanism, in order to realize compact structure, high stiffness, the unidirectional 360 degrees rotation and reverse self-locking function. The precision, stiffness, mechanical properties and reliability of the mechanism are analyzed in the paper. The results show that the position accuracy of the filter wheel can meet the requirement of 0.5mm. The first order modal of the mechanism is 313Hz. The results of vibration test indicate that stiffness, dynamic performance and reliability of the mechanism can be meet. Therefore, the design of filter wheel in this paper can ensure the multi-spectral imaging requirements under complex spatial conditions.

astro-ph.IM↗

arXiv2025

Lightweight design and analysis of optical cover plate for exoplanet imaging coronagraph

In order to reduce the load mass and solve the problem that the aluminum alloy optical cover plate of exoplanet imaging coronagraph was easy to deform, based on the equal generation design method, this paper designed and determined the configuration of the carbon fiber optical cover plate. Through the simulation of layup by finite element analysis, this paper researched the influence of different layering angles and sequences on the stiffness of optical cover plate. Finally, the carbon fiber layup method was determined as [15/-75/-15/75]s. The dynamic response analysis show that all the indexes satisfy the system requirements, and verify the feasibility of carbon fiber optical cover plate.

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arXiv2025

Optimization design and analysis for the mechanical test platform of scientific probe module of the Cool Planet Imaging Coronagraph

This paper optimizes the design and analysis of the mechanical test platform for the scientific probe module of the Cool Planet Imaging Coronagraph, which is the fifth part of the China Space Station survey Telescope. First, according to the module layout and economic requirements, the preliminary structural design of the module mechanical test platform is carried out, and the stiffness sensitive parameters of the assembly are identified to determine the optimization parameters. The Central Composite Design method is used to design the test platform, and a third-order regression model is constructed for response surface analysis. The third-order response surface model of the fundamental frequency and amplitude of the test platform is obtained by fitting the test data with the least squares method, and the structure of the module mechanical test platform is determined. The modal analysis is carried out to determine the fundamental frequency and vibration modes of the mechanical test platform. The vibration response of the platform is simulated by sine, random and swept frequency vibration simulations. The response surface fitting algorithm is verified by the test platform swept frequency test. The agreement between the response surface fitting algorithm and the experiment is good. The fundamental frequency of the test platform is 436.2Hz (>300Hz), which meets the design index requirements of the test platform and can accurately guide the optimization design work. At the same time, it provides the theoretical basis and design method for the structural design of the Chinese manned space station.

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arXiv2023

ADPBA: Efficiently generating Lagrangian cuts for two-stage stochastic integer programs

The use of Lagrangian cuts proves effective in enhancing the lower bound of the master problem within the execution of benders-type algorithms, particularly in the context of two-stage stochastic programs. However, even the process of generating a single Lagrangian cut is notably time-intensive. In light of this challenge, we present a novel framework that integrates Lagrangian cut generation with an adaptive partition-based approach, thereby mitigating this time-related drawback to a considerable extent. Furthermore, we also discuss the dominance relationship between the generated partition-based Lagrangian cut and the Lagrangian cut for the original problem. To provide empirical evidence of our approach's efficacy, we undertake an extensive computational study encompassing instances involving even up to a thousand scenarios. The results of this study conclusively demonstrate the superiority and efficiency of the proposed methodology.

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