arXiv subjects

Yitian Qian

Publications and source records attributed to Yitian Qian.

18 recordsLinked to original sources

arXiv2026

VisualLeakBench: Reproducible Action-Boundary Propagation Failures in Vision-Language Agents

Vision-language agents increasingly consume screenshots, documents, and user interfaces before writing to memory, sending messages, or invoking external tools. We study a concrete failure mode in this setting: action-boundary propagation, where sensitive or unsafe visible text is copied from an image into downstream tool arguments. We present VisualLeakBench, a diversified 500-image benchmark spanning UI, chat, document, form, and dashboard scenes, and evaluate a stratified 100-image agent subset with four production VLM systems under two workflows: note capture and external handoff. At baseline, target strings are propagated into tool arguments in 78.8% of PII cases and 85.5% of rendered unsafe-text cases. Under a defensive system prompt, rendered unsafe-text propagation remains high at 52.6%, while PII tool propagation falls to 2.0%, largely by suppressing tool use rather than preserving utility. Rates are tool-surface dependent: search-like tools suppress PII propagation, but rendered unsafe text still crosses tool boundaries. We measure visual-to-tool propagation rather than downstream instruction execution. We additionally provide a labeled-target oracle upper-bound diagnostic that localizes most failures at the tool boundary while leaving response-side leakage as residual risk.

cs.CV↗

arXiv2026

An inexact variable metric proximal linearization method for composite optimization on manifolds

This paper concerns the minimization of the composition of a nonsmooth convex function and a $\mathcal{C}^{1,1}$ mapping $F$ over a $\mathcal{C}^2$-smooth embedded closed submanifold $\mathcal{M}$. For this class of nonconvex and nonsmooth problems, we propose an inexact variable metric proximal linearization method by leveraging its composite structure and the retraction and first-order information of $\mathcal{M}$, which at each iteration seeks an inexact solution to a subspace constrained strongly convex problem by a practical inexactness criterion. Under the boundedness assumption on the iterate sequence, we establish the $O(ε^{-3})$ oracle complexity with a dual fast gradient method as the inner solver, and prove that any cluster point of the iterate sequence is a stationary point. If in addition the constructed potential function has the Kurdyka-Lojasiewicz (KL) property on the set of cluster points, the iterate sequence converges to a stationary point, and if the potential function has the KL property of exponent $q\in[\frac{1}{2},1)$, the local convergence rate is characterized. We also provide a condition only involving the original data to identify the KL property of the potential function with an exponent $q\in[0,1)$. Numerical comparisons with the existing methods validate the efficiency of the proposed method.

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arXiv2026

VisualLeakBench: Auditing the Fragility of Large Vision-Language Models against PII Leakage and Social Engineering

As Large Vision-Language Models (LVLMs) are increasingly deployed in agent-integrated workflows and other deployment-relevant settings, their robustness against semantic visual attacks remains under-evaluated -- alignment is typically tested on explicit harmful content rather than privacy-critical multimodal scenarios. We introduce VisualLeakBench, an evaluation suite to audit LVLMs against OCR Injection and Contextual PII Leakage using 1,000 synthetically generated adversarial images with 8 PII types, validated on 50 in-the-wild (IRL) real-world screenshots spanning diverse visual contexts. We evaluate four frontier systems (GPT-5.2, Claude~4, Gemini-3 Flash, Grok-4) with Wilson 95% confidence intervals. Claude~4 achieves the lowest OCR ASR (14.2%) but the highest PII ASR (74.4%), exhibiting a comply-then-warn pattern -- where verbatim data disclosure precedes any safety-oriented language. Grok-4 achieves the lowest PII ASR (20.4%). A defensive system prompt eliminates PII leakage for two models, reduces Claude~4's leakage from 74.4% to 2.2%, but has no effect on Gemini-3 Flash on synthetic data. Strikingly, IRL validation reveals Gemini-3 Flash does respond to mitigation on real-world images (50% to 0%), indicating that mitigation robustness is template-sensitive rather than uniformly absent. We release our dataset and code for reproducible robustness and safety evaluation of deployment-relevant vision-language systems.

cs.CV↗

arXiv2026

Do Deployment Constraints Make LLMs Hallucinate Citations? An Empirical Study across Four Models and Five Prompting Regimes

LLMs are increasingly used to draft academic text and to support software engineering (SE) evidence synthesis, but they often hallucinate bibliographic references that look legitimate. We study how deployment-motivated prompting constraints affect citation verifiability in a closed-book setting. Using 144 claims (24 in SE&CS) and a deterministic verification pipeline (Crossref + Semantic Scholar), we evaluate two proprietary models (Claude Sonnet, GPT-4o) and two open-weight models (LLaMA~3.1-8B, Qwen~2.5-14B) across five regimes: Baseline, Temporal (publication-year window), Survey-style breadth, Non-Disclosure policy, and their combination. Across 17,443 generated citations, no model exceeds a citation-level existence rate of 0.475; Temporal and Combo conditions produce the steepest drops while outputs remain format-compliant (well-formed bibliographic fields). Unresolved outcomes dominate (36-61%); a 100-citation audit indicates that a substantial fraction of Unresolved cases are fabricated. Results motivate post-hoc citation verification before LLM outputs enter SE literature reviews or tooling pipelines.

cs.IR↗

arXiv2026

A Relaxation Method for Nonsmooth Nonlinear Optimization with Binary Constraints

We study binary optimization problems of the form $ \min_{x\in\{-1,1\}^n} f(Ax-b) $ with possibly nonsmooth loss $f$. Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a majorization-minimization algorithm by using the difference-of-convexity (DC) reformuation for the rank-one constraint and the Moreau envelop for the nonsmooth loss. We provide global complexity guarantees for the proposed \textbf{D}ifference of \textbf{C}onvex \textbf{R}elaxation \textbf{A}lgorithm (DCRA) and show that it produces an approximately feasible binary solution with an explicit bound on the optimality gap. Numerical experiments on synthetic and real datasets confirm that our method achieves superior accuracy and scalability compared with existing approaches.

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arXiv2025

Error Bounds for Rank-one Double Nonnegative Reformulations of QAP and Exact Penalties

This paper focuses on the error bounds for several equivalent rank-one doubly nonnegative (DNN) conic reformulations of the quadratic assignment problem (QAP), a class of challenging combinatorial optimization problems. We provide three equivalent rank-one DNN reformulations of the QAP, including the one proposed in \cite{Jiang21}, and establish the locally and globally Lipschitzian error bounds for their feasible sets. Then, these error bounds are employed to prove that the penalty problems induced by the difference-of-convexity (DC) reformulation of the rank-one constraint are global exact penalties, and so are the penalty problems for their Burer-Monteiro (BM) factorizations. As a byproduct, the penalty problem for the rank-one DNN reformulation in \cite{Jiang21} is shown to be a global exact penalty without the calmness assumption. Finally, we illustrate the application of these exact penalties by proposing a relaxation approach with one of them to seek a rank-one approximate feasible solution. This relaxation approach is validated to be superior to the commercial solver Gurobi for \textbf{132} benchmark instances in terms of the relative gap between the generated objective value and the known best one and the number of instances with better objective values.

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arXiv2025

Convergence of the majorized PAM method with subspace correction for low-rank composite factorization model

This paper focuses on the convergence certificates of the majorized proximal alternating minimization (PAM) method with subspace correction, proposed in \cite{TaoQianPan22} for the column $\ell_{2,0}$-norm regularized factorization model and now extended to a class of low-rank composite factorization models from matrix completion. The convergence analysis of this PAM method becomes extremely challenging because a subspace correction step is introduced to every proximal subproblem to ensure a closed-form solution. We establish the full convergence of the iterate sequence and column subspace sequences of factor pairs generated by the PAM, under the KL property of the objective function and a condition that holds automatically for the column $\ell_{2,0}$-norm function. Numerical comparison with the popular proximal alternating linearized minimization (PALM) method is conducted on one-bit matrix completion problems, which indicates that the PAM with subspace correction has an advantage in seeking lower relative error within less time.

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arXiv2025

An inexact $q$-order regularized proximal Newton method for nonconvex composite optimization

This paper concerns the composite problem of minimizing the sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. For this class of nonconvex and nonsmooth problems, by leveraging a practical inexactness criterion and a novel selection strategy for iterates, we propose an inexact $q$-order regularized proximal Newton method for $q\in[2,3]$, which becomes an inexact cubic regularization (CR) method for $q=3$. We prove that the whole iterate sequence converges to a stationary point for the KL objective function; and when the objective function has the KL property of exponent $θ\in(0,\frac{q-1}{q})$, the convergence has a local $Q$-superlinear rate of order $\frac{q-1}{θq}$. In particular, under a local Hölderian error bound of order $γ\in(\frac{1}{q-1},1]$ on a second-order stationary point set, we show that the iterate and objective value sequences converge to a second-order stationary point and a second-order stationary value, respectively, with a local $Q$-superlinear rate of order $γ(q\!-\!1)$, specified as the $Q$-quadratic rate for $q=3$ and $γ=1$. This is the first practical inexact CR method with $Q$-quadratic convergence rate for nonconvex composite optimization. We validate the efficiency of the CR method with ZeroFPR as the inner solver by applying it to composite optimization problems with highly nonlinear $f$.

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arXiv2025

GLL-type Nonmonotone Descent Methods Revisited under Kurdyka-Łojasiewicz Property

The purpose of this paper is to extend the full convergence results of the classic GLL-type (Grippo-Lampariello-Lucidi) nonmonotone methods to nonconvex and nonsmooth optimization. We propose a novel iterative framework for the minimization of a proper and lower semicontinuous function $Φ$. The framework consists of the GLL-type nonmonotone decrease condition for a sequence, a relative error condition for its augmented sequence with respect to a Kurdyka-Łojasiewicz (KL) function $Θ$, and a relative gap condition for the partial maximum objective value sequence. The last condition is shown to be a product of the prox-regularity of $Φ$ on the set of cluster points, and to hold automatically under a mild condition on the objective value sequence. We prove that for any sequence and its bounded augmented sequence together falling within the framework, the sequence itself is convergent. Furthermore, when $Θ$ is a KL function of exponent $θ\in(0, 1)$, the convergence admits a linear rate if $θ\in(0, 1/2]$ and a sublinear rate if $θ\in(1/2, 1)$. As applications, we prove, for the first time, that the two existing algorithms, namely the nonmonotone proximal gradient (NPG) method with majorization and NPG with extrapolation both enjoy the full convergence of the iterate sequences for nonconvex and nonsmooth KL composite optimization problems.

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arXiv2025

Error bound and exact penalty method for optimization problems with nonnegative orthogonal constraint

This paper is concerned with a class of optimization problems with the nonnegative orthogonal constraint, in which the objective function is $L$-smooth on an open set containing the Stiefel manifold ${\rm St}(n,r)$. We derive a locally Lipschitzian error bound for the feasible points without zero rows when $n>r>1$, and when $n>r=1$ or $n=r$ achieve a global Lipschitzian error bound. Then, we show that the penalty problem induced by the elementwise $\ell_1$-norm distance to the nonnegative cone is a global exact penalty, and so is the one induced by its Moreau envelope under a lower second-order calmness of the objective function. A practical penalty algorithm is developed by solving approximately a series of smooth penalty problems with a retraction-based nonmonotone line-search proximal gradient method, and any cluster point of the generated sequence is shown to be a stationary point of the original problem. Numerical comparisons with the ALM \citep{Wen13} and the exact penalty method \citep{JiangM22} indicate that our penalty method has an advantage in terms of the quality of solutions despite taking a little more time.

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arXiv2024

Convergence of ZH-type nonmonotone descent method for Kurdyka-Łojasiewicz optimization problems

We propose a novel iterative framework for minimizing a proper lower semicontinuous Kurdyka-Łojasiewicz (KL) function $Φ$. It comprises a Zhang-Hager (ZH-type) nonmonotone decrease condition and a relative error condition. Hence, the sequence generated by the ZH-type nonmonotone descent methods will fall within this framework. Any sequence conforming to this framework is proved to converge to a critical point of $Φ$. If in addition $Φ$ has the KL property of exponent $θ\!\in(0,1)$ at the critical point, the convergence has a linear rate for $θ\in(0,1/2]$ and a sublinear rate of exponent $\frac{1-θ}{1-2θ}$ for $θ\in(1/2,1)$. To the best of our knowledge, this is the first work to establish the full convergence of the iterate sequence generated by a ZH-type nonmonotone descent method for nonconvex and nonsmooth optimization problems. The obtained results are also applied to achieve the full convergence of the iterate sequences produced by the proximal gradient method and Riemannian gradient method with the ZH-type nonmonotone line-search.

math.OC↗

arXiv2024

A relaxation method for binary optimizations on constrained Stiefel manifold

This paper focuses on a class of binary orthogonal optimization problems frequently arising in semantic hashing. Consider that this class of problems may have an empty feasible set, rendering them not well-defined. We introduce an equivalent model involving a restricted Stiefel manifold and a matrix box set, and then investigate its penalty problems induced by the $\ell_1$-distance from the box set and its Moreau envelope. The two penalty problems are always well-defined. Moreover, they serve as the global exact penalties provided that the original feasible set is non-empty. Notably, the penalty problem induced by the Moreau envelope is a smooth optimization over an embedded submanifold with a favorable structure. We develop a retraction-based line-search Riemannian gradient method to address the penalty problem. Finally, the proposed method is applied to supervised and unsupervised hashing tasks and is compared with several popular methods on the MNIST and CIFAR-10 datasets. The numerical comparisons reveal that our algorithm is significantly superior to other solvers in terms of feasibility violation, and it is comparable even superior to others in terms of evaluation metrics related to the Hamming distance.

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arXiv2023

A Superlinear Convergence Framework for Kurdyka-Łojasiewicz Optimization

This work extends the iterative framework proposed by Attouch et al. (in Math. Program. 137: 91-129, 2013) for minimizing a nonconvex and nonsmooth function $Φ$ so that the generated sequence possesses a Q-superlinear convergence rate. This framework consists of a monotone decrease condition, a relative error condition and a continuity condition, and the first two conditions both involve a parameter $p\!>0$. We justify that any sequence conforming to this framework is globally convergent when $Φ$ is a Kurdyka-Łojasiewicz (KL) function, and the convergence has a Q-superlinear rate of order $\frac{p}{θ(1+p)}$ when $Φ$ is a KL function of exponent $θ\in(0,\frac{p}{p+1})$. Then, we illustrate that the iterate sequence generated by an inexact $q\in[2,3]$-order regularization method for composite optimization problems with a nonconvex and nonsmooth term belongs to this framework, and consequently, first achieve the Q-superlinear convergence rate of order $4/3$ for an inexact cubic regularization method to solve this class of composite problems with KL property of exponent $1/2$.

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arXiv2022

Convergence of a class of nonmonotone descent methods for KL optimization problems

This paper is concerned with a class of nonmonotone descent methods for minimizing a proper lower semicontinuous KL function $Φ$, which generates a sequence satisfying a nonmonotone decrease condition and a relative error tolerance. Under suitable assumptions, we prove that the whole sequence converges to a limiting critical point of $Φ$ and, when $Φ$ is a KL function of exponent $θ\in[0,1)$, the convergence admits a linear rate if $θ\in[0,1/2]$ and a sublinear rate associated to $θ$ if $θ\in(1/2,1)$. The required assumptions are shown to be sufficient and necessary if $Φ$ is also weakly convex on a neighborhood of stationary point set. Our results resolve the convergence problem on the iterate sequence generated by a class of nonmonotone line search algorithms for nonconvex and nonsmooth problems, and also extend the convergence results of monotone descent methods for KL optimization problems. As the applications, we achieve the convergence of the iterate sequence for the nonmonotone line search proximal gradient method with extrapolation and the nonmonotone line search proximal alternating minimization method with extrapolation. Numerical experiments are conducted for zero-norm and column $\ell_{2,0}$-norm regularized problems to validate their efficiency.

math.OC↗

arXiv2022

Calmness of partial perturbation to composite rank constraint systems and its applications

This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type error bound and also a global Lipschitz-type error bound under a certain compactness. Based on its lifted formulation, we derive two criteria for identifying those closed sets such that the associated partial perturbation possesses the calmness, and provide a collection of examples to demonstrate that the criteria are satisfied by common nonnegative and positive semidefinite rank constraint sets. Then, we use the calmness of this perturbation to obtain several global exact penalties for rank constrained optimization problems, and a family of equivalent DC surrogates for rank regularized problems.

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arXiv2021

Column $\ell_{2,0}$-norm regularized factorization model of low-rank matrix recovery and its computation

This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of factors and low-rank solutions. For this nonconvex discontinuous optimization problem, we develop an alternating majorization-minimization (AMM) method with extrapolation, and a hybrid AMM in which a majorized alternating proximal method is proposed to seek an initial factor pair with less nonzero columns and the AMM with extrapolation is then employed to minimize of a smooth nonconvex loss. We provide the global convergence analysis for the proposed AMM methods and apply them to the matrix completion problem with non-uniform sampling schemes. Numerical experiments are conducted with synthetic and real data examples, and comparison results with the nuclear-norm regularized factorization model and the max-norm regularized convex model show that the column $\ell_{2,0}$-regularized factorization model has an advantage in offering solutions of lower error and rank within less time.

math.OC↗

arXiv2021

A relaxation approach to UBPPs based on equivalent DC penalized factorized matrix programs

This paper is concerned with the unconstrained binary polynomial program (UBPP), which has a host of applications in many science and engineering fields. By leveraging the global exact penalty for its DC constrained SDP reformulation, we achieve an equivalent DC penalized SDP, and propose a continuous relaxation approach by seeking the critical point of the Burer-Monteiro factorization for a finite number of DC penalized SDPs with increasing penalty factors. A globally convergent majorization-minimization (MM) method with extrapolation is also developed to capture such critical points. Under a mild condition, we show that the rank-one projection of the output for the relaxation approach is an approximate feasible solution of the UBPP and quantify the upper bound of its objective value from the optimal value. Numerical comparisons with the SDP relaxation method armed with a special random rounding technique and the DC relaxation approach based on the solution of linear SDPs confirm the efficiency of the proposed relaxation approach, which can solve the instance of \textbf{20000} variables in \textbf{15} minutes and yield an upper bound to the optimal value and the known best value with a relative error at most \textbf{1.824\%} and \textbf{2.870\%}, respectively.

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arXiv2021

An inexact PAM method for computing Wasserstein barycenter with unknown supports

Wasserstein barycenter is the centroid of a collection of discrete probability distributions which minimizes the average of the $\ell_2$-Wasserstein distance. This paper focuses on the computation of Wasserstein barycenters under the case where the support points are free, which is known to be a severe bottleneck in the D2-clustering due to the large-scale and nonconvexity. We develop an inexact proximal alternating minimization (iPAM) method for computing an approximate Wasserstein barycenter, and provide its global convergence analysis. This method can achieve a good accuracy with a reduced computational cost when the unknown support points of the barycenter have low cardinality. Numerical comparisons with the 3-block B-ADMM in \cite{YeWWL17} and an alternating minimization method involving the LP subproblems on synthetic and real data show that the proposed iPAM can yield comparable even a little better objective values in less CPU time, and hence the computed barycenter will render a better role in the D2-clustering.

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