arXiv subjects

Zhou Wei

Publications and source records attributed to Zhou Wei.

At least 19 recordsLinked to original sources

arXiv2026

New Outer Approximation Algorithms for Nonsmooth Convex MINLP Problems

This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When the subproblem is feasible, valid linear cuts are derived by computing suitable subgradients of the objective and constraint functions at the optimal solution, utilizing KKT optimality conditions. A new parameter, defined through the nonlinear constraint functions, is introduced to facilitate the generation of these cuts. For infeasible subproblems, a feasibility problem is solved, and valid linear cuts are generated via KKT-based subgradients to exclude the infeasible integer assignment. By integrating both types of cuts, a mixed-integer linear programming (MILP) master problem is formulated and proven equivalent to the original MINLP. This equivalence underpins a new outer approximation algorithm, which is guaranteed to terminate after a finite number of iterations. Numerical experiments on smooth convex MINLP problems demonstrate that the proposed algorithm produces tighter MILP relaxations than the classical outer approximation method. Furthermore, the approach offers an alternative mechanism for generating linear cuts, extending beyond reliance solely on first-order Taylor expansions and shows that the efficiency of outer approximation algorithm is strongly dependent on the inherent structure of the MINLP problem.

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arXiv2026

UniX: Unifying Autoregression and Diffusion for Chest X-Ray Understanding and Generation

Despite recent progress, medical foundation models still struggle to unify visual understanding and generation, as these tasks have inherently conflicting goals: semantic abstraction versus pixel-level reconstruction. Existing approaches, typically based on parameter-shared autoregressive architectures, frequently lead to compromised performance in one or both tasks. To address this, we present UniX, a next-generation unified medical foundation model for chest X-ray understanding and generation. UniX decouples the two tasks into an autoregressive branch for understanding and a diffusion branch for high-fidelity generation. Crucially, a cross-modal self-attention mechanism is introduced to dynamically guide the generation process with understanding features. Coupled with a rigorous data cleaning pipeline and a multi-stage training strategy, this architecture enables synergistic collaboration between tasks while leveraging the strengths of diffusion models for superior generation. On two representative benchmarks, UniX achieves a 46.1% improvement in understanding performance (Micro-F1) and a 24.2% gain in generation quality (FD-RadDino), using only a quarter of the parameters of LLM-CXR. By achieving performance on par with task-specific models, our work establishes a scalable paradigm for synergistic medical image understanding and generation. Codes and models are available at https://github.com/ZrH42/UniX.

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arXiv2025

OpenGround: Planning-based Online Perception for Open-World 3D Visual Grounding

3D visual grounding aims to locate objects based on natural language descriptions in 3D scenes. Existing supervised methods are limited by generalization and recent zero-shot methods typically rely on a predefined Object Lookup Table (OLT) to query Visual Language Models (VLMs) for reasoning about object locations via a single step grounding, which limits the applications in scenarios with undefined targets and complex queries. To address these problems, we present OpenGround, a novel zero-shot framework for open-world 3D visual grounding that remains compatible with recent zero-shot methods. OpenGround integrates Task-Chain Planning to decompose a query into a plan of context-to-target sub-goals for progressive grounding, and Context-Guided Perception to perceive novel objects online under context guidance from the task chain. We also propose a new dataset named OpenTarget, which contains over 7000 object-description pairs to mimic open-world evaluation. Extensive experiments demonstrate that OpenGround achieves competitive performance on Nr3D, state-of-the-art on ScanRefer, and delivers a substantial 17.6\% improvement on OpenTarget. Project Page at https://why-102.github.io/openground.io/.

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arXiv2025

Complexity of Error Bounds for Systems of Linear Inequalities

Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary point to the solution set of a linear system. Despite this long history, relatively little is known about the intrinsic computational complexity of error bounds. In this paper, we investigate the complexity of error bounds for systems of linear inequalities. We first reformulate the problem as a finite collection of min--max optimization problems defined on the unit sphere and associated with subsets of the rows of the given matrix. We then prove that the problem does not belong to the class {\bf P}, while it is {\bf co\mbox{-}NP}-complete. Furthermore, we establish the existence of a pseudo-polynomial-time algorithm for solving the complementary problem. In particular, the complement may be regarded as a number problem, although it is not {\bf NP}-complete in the strong sense unless {\bf P} = {\bf NP}.

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arXiv2025

Metric Subregularity of Multifunctions and Applications to Characterizations of Asplund Spaces

In this paper, we investigate metric subregularity of multifunctions between Asplund spaces. Using Mordukhovich normal cones and coderivatives, we introduce the limiting Basic Constraint Qualification (BCQ) associated with a given multifunction. This BCQ provides necessary dual conditions for the metric subregularity of multifunctions in the Asplund space setting. Furthermore, we establish characterizations of Asplund spaces in terms of the limiting BCQ condition implied by metric subregularity. By employing Frechet normal cones and coderivatives, we derive necessary dual conditions for metric subregularity expressed as fuzzy inclusions, and we also obtain characterizations of Asplund spaces via these fuzzy inclusions. As an application, we examine metric subregularity of the conic inequality defined by a vector-valued function and a closed (not necessarily convex) cone with a nontrivial recession cone. By using Mordukhovich and Frechet subdifferentials relative to the given cone, we establish necessary dual conditions for the metric subregularity of such inequalities in Asplund spaces. The results based on Mordukhovich subdifferentials characterize Asplund spaces, while those based on Frechet subdifferentials yield necessary or sufficient conditions for Asplund spaces. These conditions recover, as special cases, the known error-bound results for inequalities defined by extended-real-valued functions on Asplund spaces. Overall, this work highlights that the validity of necessary conditions formulated via normal cones and subdifferentials for error bounds of convex or nonconvex inequalities depends crucially on the Asplund property of the underlying space.

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arXiv2024

Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces

In this paper, we mainly study subtransversality and two types of strong CHIP (given via Fréchet and limiting normal cones) for a collection of finitely many closed sets. We first prove characterizations of Asplund spaces in terms of subtransversality and intersection formulae of Fréchet normal cones. Several necessary conditions for subtransversality of closed sets are obtained via Fréchet/limiting normal cones in Asplund spaces. Then, we consider subtransversality for some special closed sets in convex-composite optimization. In this frame we prove an equivalence result on subtransversality, strong Fréchet CHIP and property (G) so as to extend a duality characterization of subtransversality of finitely many closed convex sets via strong CHIP and property (G) to the possibly non-convex case. As applications, we use these results on subtransversality and strong CHIP to study error bounds of inequality systems and give several dual criteria for error bounds via Fréchet normal cones and subdifferentials.

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arXiv2024

Perturbation Analysis of Error Bounds for Convex Functions on Banach Spaces

This paper focuses on the stability of both local and global error bounds for a proper lower semicontinuous convex function defined on a Banach space. Without relying on any dual space information, we first provide precise estimates of error bound moduli using directional derivatives. For a given proper lower semicontinuous convex function on a Banach space, we prove that the stability of local error bounds under small perturbations is equivalent to the directional derivative at a reference point having a non-zero minimum over the unit sphere. Additionally, the stability of global error bounds is shown to be equivalent to the infimum of the directional derivatives, at all points on the boundary of the solution set, being bounded away from zero over some neighborhood of the unit sphere.

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arXiv2024

Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems

In this paper, we mainly study error bounds for a single convex inequality and semi-infinite convex constraint systems, and give characterizations of stability of error bounds via directional derivatives. For a single convex inequality, it is proved that the stability of local error bounds under small perturbations is essentially equivalent to the non-zero minimun of the directional derivative at a reference point over the sphere, and the stability of global error bounds is proved to be equivalent to the strictly positive infimum of the directional derivatives, at all points in the boundary of the solution set, over the sphere as well as some mild constraint qualification. When these results are applied to semi-infinite convex constraint systems, characterizations of stability of local and global error bounds under small perturbations are also provided. In particular such stability of error bounds is proved to only require that all component functions in semi-infinite convex constraint systems have the same linear perturbation. Our work demonstrates that verifying the stability of error bounds for convex inequality constraint systems is, to some degree, equivalent to solving the convex optimization/minimization problems (defined by directional derivatives) over the sphere.

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arXiv2023

On Error Bounds of Inequalities in Asplund Spaces

Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error bounds of a general inequality defined by a proper lower semicontinuous function on an Asplund space. Even though the results of the dual characterization on the error bounds of a general inequality (if one drops the convexity assumption) may not be valid, several necessary dual conditions are still obtained in terms of Fréchet/Mordukhovich subdifferentials of the concerned function at points in the solution set. Moreover, for an inequality defined by a composite-convex function that is to say by a function which is the composition of a convex function with a smooth mapping, such dual conditions also turn out to be sufficient to have the error bound property. Our work is an extension of results on dual characterizations of convex inequalities to the possibly non-convex case.

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arXiv2023

Primal Characterizations of Stability of Error Bounds for Semi-infinite Convex Constraint Systems in Banach Spaces

This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are subject to small perturbations. These characterizations are given in terms of the directional derivatives of the functions that enter into the definition of these systems. It is proved that the stability of error bounds is essentially equivalent to verifying that the optimal values of several minimax problems, defined in terms of the directional derivatives of the functions defining these systems, are outside of some neighborhood of zero. Moreover, such stability only requires that all component functions entering the system have the same linear perturbation. When these stability results are applied to the sensitivity analysis of Hoffman's constants for semi-infinite linear systems, primal criteria for Hoffman's constants to be uniformly bounded under perturbations of the problem data are obtained.

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arXiv2022

Primal Characterizations of Error Bounds for Composite-convex Inequalities

This paper is devoted to primal conditions of error bounds for a general function. In terms of Bouligand tangent cones, lower Hadamard directional derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several necessary and/or sufficient conditions of error bounds with mild assumptions. Then we use these primal results to characterize error bounds for composite-convex functions (i.e. the composition of a convex function with a continuously differentiable mapping). It is proved that the primal characterization of error bounds can be established via Bouligand tangent cones, directional derivatives and the Hausdorff-Pompeiu excess if the mapping is metrically regular at the given point. The accurate estimate on the error bound modulus is also obtained.

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arXiv2019

On Riemann Integration in Metrizable Vector Spaces

In classical analysis, Lebesgue first proved that $\mathbb{R}$ has the property that each Riemann integrable function from $[a,b]$ into $\mathbb{R}$ is continuous almost everywhere. This property is named as the Lebesgue property. Though the Lebesgue property may be breakdown in many infinite dimensional spaces including Banach or quasi Banach spaces, to determine spaces having this property is still an interesting problem. In this paper, we study Riemann integration for vector-value functions in metrizable vector spaces and prove the fundamental theorems of calculus and primitives for continuous functions. Further we discovery that $\mathbb{R}^ω$, the countable infinite product of $\mathbb{R}$ with itself equipped with the product topology, is a metrizable vector space having the Lebesgue property and prove that $l^p(1<p\leq+\infty)$, as subspaces of $\mathbb{R}^ω$, possess the Lebesgue property although they are Banach spaces having no such property.

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arXiv2017

On Constraint Qualifications of a Nonconvex Inequality

In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials. Several conditions for these constraint qualifications are also provided therein. When restricted to the convex inequality, these constraint qualifications reduce to basic constraint qualification (BCQ) and strong BCQ studied in [SIAM J. Optim., 14(2004), 757-772] and [Math. Oper. Res., 30 (2005), 956-965].

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arXiv2016

On Metric Subregularity for Convex Constraint Systems by Primal Equivalent Conditions

In this paper, we mainly study metric subregularity for a convex constraint system defined by a convex set-valued mapping and a convex constraint subset. The main work is to provide several primal equivalent conditions for metric subregularity by contingent cone and graphical derivative. Further it is proved that these primal equivalent conditions can characterize strong basic constraint qualification of convex constraint system given by Zheng and Ng [SIAM J. Optim., 18(2007), pp. 437-460].

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arXiv2016

Second-order Optimality Conditions by Generalized Derivatives and Applications in Hilbert Spaces

In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality conditions for paraconcave functions. As applications, we use these second-order optimality conditions to study strict local minimizers of order two and provide sufficient and/or necessary conditions for ensuring the local minimizer. This work extends and generalizes the study on second-order optimality conditions from the finite-dimensional space to the Hilbert space.

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arXiv2015

Generalized Benders Decomposition for one Class of MINLPs with Vector Conic Constraint

In this paper, we mainly study one class of mixed-integer nonlinear programming problems (MINLPs) with vector conic constraint in Banach spaces. Duality theory of convex vector optimization problems applied to this class of MINLPs is deeply investigated. With the help of duality, we use the generalized Benders decomposition method to establish an algorithm for solving this MINLP. Several convergence theorems on the algorithm are also presented. The convergence theorems generalize and extend the existing results on MINLPs in finite dimension spaces.

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arXiv2015

Convex mixed integer nonlinear programming problems and an outer approximation algorithm

In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.

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arXiv2015

BCQ and Strong BCQ for Nonconvex Generalized Equations with Applications to Metric Subregularity

In this paper, based on basic constraint qualification (BCQ) and strong BCQ for convex generalized equation, we are inspired to further discuss constraint qualifications of BCQ and strong BCQ for nonconvex generalized equation and then establish their various characterizations. As applications, we use these constraint qualifications to study metric subregularity of nonconvex generalized equation and provide necessary and/or sufficient conditions in terms of constraint qualifications considered herein to ensure nonconvex generalized equation having metric subregularity.

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