arXiv subjects

Yu-Hong Dai

Publications and source records attributed to Yu-Hong Dai.

At least 19 recordsLinked to original sources

arXiv2026

Hyperspectral Anomaly Detection via Group Sparse Low-Rank Tensor Factorization With Automatic Anomaly Grouping

Low-rank tensor modeling has become an effective tool for hyperspectral anomaly detection. However, existing methods still suffer from high computational cost and limited flexibility in characterizing spatially structured anomalies. To address these issues, this paper proposes a hyperspectral anomaly detection method based on group sparse low-rank tensor factorization with automatic anomaly grouping (GSAA). Specifically, the low tubal rank background is characterized by imposing group sparsity on tensor factors, which provides an efficient alternative to direct tensor rank regularization. For anomaly modeling, a latent grouping map is introduced to build an automatic anomaly grouping penalty, allowing anomaly groups to be adaptively inferred from the data rather than predefined at the pixel level. To further exploit complementary spectral and spatial information, GSAA is applied in both domains, and the resulting detection maps are fused to form a spectral--spatial version of GSAA, termed GSAA-SS. An efficient linearized alternating direction method of multipliers algorithm with convergence guarantee is developed to solve the resulting model. Experimental results on five real hyperspectral datasets demonstrate that the proposed method achieves superior detection performance and competitive computational efficiency compared with several state-of-the-art methods.

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arXiv2026

A Multi-View Coupled Tensor Decomposition for Lightweight Online Adaptive Traffic Prediction

Accurate online traffic prediction is essential for intelligent transportation systems, where forecasting must be performed continuously under imperfect sensing conditions. Missing observations and anomalous disturbances make this task challenging, particularly when prediction relies on a single traffic view. This paper proposes a Multi-View Coupled Tensor Decomposition (MVCTD) model for online traffic prediction from imperfect multi-view observations, such as speed, flow, and occupancy. The proposed model uses coupled tensor decomposition to build a structured latent forecasting space, in which shared spatial structures across traffic views and view-specific temporal dynamics are jointly modeled. A group sparse regularization is further introduced to capture correlated abnormal responses induced by real traffic anomalies and thus reduce their influence on forecasts. For streaming deployment, MVCTD performs iterative refinement only on the current latent tensor, while the remaining model variables are updated by lightweight closed-form steps based on summarized historical information, thereby avoiding repeated optimization over the full historical sequence. Experiments on real-world traffic datasets demonstrate that MVCTD achieves accurate forecasts with favorable runtime under severe missingness, confirming its suitability for online traffic prediction.

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arXiv2026

A Multiscale Primal-Dual Interior-Point Relaxation Method for Large-Scale Optimal Transport Problems

Large-scale optimal transport (OT) problems involve a vast number of transport variables, leading to prohibitive memory and computational costs. To address these challenges, we propose a multiscale primal-dual interior-point relaxation method (MSIPRM). The multiscale outer framework constructs a hierarchy of standard OT problems at progressively finer levels. At each level, the OT problem is solved over a sequence of adaptively refined active sets initialized based on the solution support at the previous level. This yields a sequence of closely related sparse subproblems, thereby substantially reducing memory requirements. The primal-dual interior-point relaxation method (IPRM) serves as the inner solver for each sparse subproblem. Since IPRM does not require strictly interior iterates, it can readily use the solution of the previous subproblem as a warm start. To efficiently obtain the Newton direction, we solve a reduced Schur complement system derived from the normal equations. Furthermore, we develop an effective support-identification strategy based on the approximate solutions obtained by IPRM. We establish condition number estimates for the Schur complement matrices and analyze the global and local convergence properties of the algorithm. Numerical experiments on large-scale test problems demonstrate the computational efficiency and scalability of MSIPRM and show that it compares favorably with existing solvers. In particular, MSIPRM can handle instances whose full formulations contain trillions of transport variables.

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arXiv2026

A primal--dual interior-point method for nonsymmetric conic optimization with conjugate-free scaling

We develop a primal--dual interior-point method for nonsymmetric conic optimization based on a conjugate-free scaling matrix. The scaling is obtained from a single-secant BFGS update of the primal barrier Hessian. In contrast to multi-secant BFGS scalings, it does not require conjugate-barrier derivatives. This feature is important for high-dimensional nonsymmetric cones, where conjugate-barrier derivatives may be unavailable in closed form or expensive to compute. We embed the conjugate-free scaling in a homogeneous self-dual predictor--corrector framework. Using a split central-path neighborhood that separately controls the conic variables and the scalar homogeneous variables, we prove that the scaling matrix remains uniformly comparable to the primal barrier Hessian. This comparison bound is used to prove neighborhood preservation and to show that the complementarity measure and the linear residual decrease at a uniform rate. Consequently, the method attains an iteration bound of $\mathcal{O}(\sqrt{\nu}\log(1/\varepsilon))$, improving the $\mathcal{O}(\nu\log(1/\varepsilon))$ bound of Badenbroek and Dahl [Optim. Methods Softw., 37 (2022), pp. 1027--1064] and matching the best-known complexity order for interior-point methods. Numerical experiments on instances involving the operator perspective epigraph cone and the quantum relative entropy cone show that the method is competitive with QICS, a specialized solver for conic models arising in quantum information.

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arXiv2026

Enhancing Presolve in Mixed Integer Programming by Combining Probing and Dual Fixing

Probing and dual fixing are two powerful presolve techniques in mixed integer programming (MIP) solvers. Probing tentatively sets some binary variables to 0 or 1, applies linear constraint based domain propagation techniques to derive better variable bounds, and extracts useful information such as stronger variable implications and better global variable bounds. Dual fixing attempts to fix variables to lower or upper bounds while ensuring that at least one optimal solution is retained, as long as the problem was feasible. In this paper, we investigate how to combine the two approaches in MIP solvers to achieve a better performance. In particular, we first embed dual fixing into the probing framework, deriving more useful variables' implications for enhancing the capability of probing. Then, we develop an improved dual fixing technique where more variable fixings can be applied, and use the probing framework to detect the reductions. Computational results on the MIPLIB 2017 benchmark instances demonstrate the potential of the two proposed techniques in combining probing and dual fixing on the open-source MIP solver HiGHS.

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arXiv2026

Exploiting Variable Implications in Presolve for Mixed Integer Programming

Presolve for mixed integer programming (MIP) problems aims to eliminate redundant information, strengthen the formulation, and extract useful structural information for the subsequent branch-and-cut process. An important type of such structural information is the variable implications (VIs), which describe how a bound on a variable depends on a bound of a binary variable. In this paper, we develop two new presolve techniques that exploit VIs to derive reductions for MIP problems. The first technique, called VI aggregation, aggregates multiple VIs into a single inequality by using implications between a variable and a set of binary variables that form a clique. This aggregation can reduce the number of constraints and tighten the linear programming relaxation. The second technique, called VI-aware linear constraint propagation (LCP), builds on the standard LCP but incorporates VIs associated with the variable being tightened to derive more reductions and can derive tighter variable bounds. We show that although VI information is additionally considered, the tightest lower or upper bound of a variable can still be derived in linear time. Moreover, compared with a state-of-the-art approach in the literature, the proposed VI-aware LCP can derive tighter variable bounds. Computational results on MIPLIB 2017 benchmark instances demonstrate the effectiveness of VI aggregation and VI-aware LCP in improving the performance of the open-source MIP solver HiGHS. In particular, using the two proposed presolve techniques, a reduction of 4% in solving time and 6% in node number on HiGHS can be achieved.

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arXiv2026

A Stochastic Implicit Proximal Point Algorithm for Solving Linearly Constrained Stochastic Minimax Problems

This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in two cases -- with or without replacement. The semismooth Newton methods with Armijo line search is used to solve the implicit proximal point update subproblem in each iteration. The algorithm efficiently handles the strongly-convex-strongly-concave objective function with nonsmooth regularizers and coupling linear equations, which is proved to exhibit global q-linear convergence of the iterations to the saddle point and global r-linearly convergence of the multipliers to the multiplier set in expectation. Numerical experiments on machine learning problems demonstrate the superiority of the proposed method over state-of-the-art algorithms in terms of both computational efficiency and selection of the step sizes.

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arXiv2026

Polynomial iteration complexity of a path-following smoothing Newton method for symmetric cone programming

It has long remained open whether smoothing Newton methods (SNMs) for symmetric cone programming (SCP) admit polynomial iteration complexity. A key difficulty lies in the lack of an analogue of the self-concordant convex framework underlying interior-point methods (IPMs). In this paper, inspired by Nemirovski's self-concordant convex-concave theory, we address this open problem by introducing a reduced barrier augmented Lagrangian (BAL) function. We prove that the reduced BAL function is self-concordant convex-concave and establish that the parameterized smooth system arising in SNMs coincides with the first-order optimality conditions of an associated minimax problem. Motivated by this equivalence, we propose a path-following smoothing Newton method (PFSNM). The reduced BAL function induces a central path and an associated neighborhood, which provide estimates for the Newton decrement needed for the path-following analysis. As a result, the method achieves an iteration complexity of $\mathcal{O}(\sqrt{\nu}\ln(1/\varepsilon))$, matching the best-known short-step complexity for IPMs. Numerical results on standard benchmarks show that PFSNM is competitive with several well-known interior-point solvers, and the observed performance is consistent with the theoretical development.

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arXiv2026

Efficient exact sequential lifting algorithm for binary knapsack set

Lifting is a crucial technique in mixed integer programming (MIP) for generating strong valid inequalities, which serve as cutting planes to improve the branch-and-cut algorithm. We first propose an exact sequential lifting algorithm for the binary knapsack set, which employs the dominance list structure to remove redundant storage and computation in the dynamic programming (DP) array. This structure preserves scale invariance and effectively handles constraints with non-integer coefficients. Then, a reduction method is developed for the lifting procedure under some conditions, further enhancing computational efficiency. Finally, numerical experiments demonstrate that the proposed algorithm outperforms DP with arrays in terms of both efficiency and stability, particularly for large-scale and large-capacity instances. Moreover, it enables exact sequential lifting for binary knapsack sets with non-integer weights and large capacities, making it directly applicable in modern MIP solvers.

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arXiv2026

On strong valid inequalities for a class of mixed-integer nonlinear sets with box constraints

In this paper, we investigate the mixed-integer nonlinear set with box constraints $X = \{(w,x)\in R\times Z^n:w\leq f(a^Tx),0\leq x\leq \mu\}$, where $f$ is a univariate concave function, $a\in R^n$, and $\mu\in Z^n_{++}$. This set arises as a substructure in many mixed-integer nonlinear optimization models and encompasses, as special cases, several previously investigated mixed-integer sets, namely the submodular maximization set, the mixed-integer knapsack set, and the mixed-integer polyhedral conic set. We present the first comprehensive polyhedral study of conv($X$). In particular, we derive a class of seed inequalities for a two-dimensional restriction of $X$, obtained by fixing all but one of the $x$ variables to their bounds in $X$, and develop two lifting procedures to obtain strong valid inequalities for conv($X$). In the first lifting procedure, we derive a subadditive approximation for the exact lifting function of the seed inequalities, and lift all fixed variables in a single phase. In the second lifting procedure, we first lift variables fixed at their lower bounds before those at their upper bounds (and vice versa), using subadditive exact and approximation lifting functions, respectively. The derived single- and two-phase lifted inequalities are shown to be facet-defining for conv($X$) under mild conditions. Moreover, for the aforementioned special cases of conv($X$), we show that the proposed lifted inequalities can either unify existing strong valid inequalities or yield new facet-defining inequalities. Finally, extensive computational experiments on expected utility maximization and weapon-target assignment problems demonstrate that the proposed lifted inequalities can substantially strengthen the continuous relaxations and significantly improve the overall computational performance of branch-and-cut algorithms.

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arXiv2026

Polyhedral results for two classes of submodular sets with GUB constraints

In this paper, we investigate the polyhedral structure of two submodular sets with generalized upper bound (GUB) constraints, which arise as important substructures in various real-world applications. We derive a class of strong valid inequalities for the two sets using sequential lifting techniques. The proposed lifted inequalities are facet-defining for the convex hulls of two sets and are stronger than the well-known extended polymatroid inequalities (EPIs). We provide a more compact characterization of these inequalities and show that each of them can be computed in linear time. Moreover, the proposed lifted inequalities, together with bound and GUB constraints, can completely characterize the convex hulls of the two sets, and can be separated using a combinatorial polynomial-time algorithm. Finally, computational results on probabilistic covering location and multiple probabilistic knapsack problems demonstrate the superiority of the proposed lifted inequalities over the EPIs within a branch-and-cut framework.

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arXiv2026

A sequential linear complementarity problem method for generalized Nash equilibrium problems

Generalized Nash equilibrium problems (GNEPs) arise in various applications where multiple players minimize individual cost functions subject to coupled constraints. A relatively unexplored approach to solving such problems is via a sequence of (mixed) linear complementarity problems (LCPs). Compared with the nonlinear equilibrium subproblems arising in recently popular penalty-based methods such as augmented Lagrangian methods, these LCPs are often substantially easier to solve. However, the existing literature on this approach is very limited, largely because of the difficulty of assessing the search directions generated by the subproblems and establishing a principled step-length acceptance criterion. This paper proposes a sequential linear complementarity problem (SLCP) method with a comprehensive convergence analysis. To assess the search directions, we introduce a novel merit function analogous to the $\ell_1$ penalty function in sequential quadratic programming. The merit function is shown to decrease along the search directions generated by the subproblems under suitable assumptions, thereby guaranteeing the global convergence of the SLCP method. We further establish local quadratic convergence and analyze the solvability of the subproblems. Preliminary numerical results demonstrate the effectiveness and competitiveness of the proposed method relative to existing approaches.

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arXiv2025

A Surrogate Value Function Formulation for Bilevel Optimization

The value function formulation captures the hierarchical nature of bilevel optimization through the optimal value function of the lower level problem, yet its implicit and nonsmooth characteristics pose significant analytical and computational difficulties. We introduce a surrogate value function formulation that replaces the intractable value function with an explicit surrogate derived from lower level stationarity conditions. This surrogate formulation preserves the essential idea of the classical value function model but fundamentally departs from Karush Kuhn Tucker (KKT) formulations, which embed lower level stationary points into the upper level feasible region and obscure the hierarchical dependence. Instead, it enforces the hierarchy through a dominance constraint that remains valid even when lower level constraint qualifications fail at the solution. We establish equivalence with the original bilevel problem, reveal the failure of standard constraint qualifications, and show that its strong stationarity implies that of KKT models. To handle the complementarity constraints in the surrogate formulation, we apply a smoothing barrier augmented Lagrangian method and prove its convergence to solutions and Clarke stationary points. Extensive experiments demonstrate the robustness and high numerical precision of this formulation, especially in nonconvex settings, including the classical Mirrlees problem where KKT models fail.

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arXiv2025

An efficient branch-and-cut approach for the sequential competitive facility location problem under partially binary rule

We investigate the sequential competitive facility location problem (SCFLP) under partially binary rule where two companies sequentially open a limited number of facilities to maximize their market shares, requiring customers to patronize, for each company, the facility with the highest utility. The SCFLP is a bilevel mixed integer nonlinear programming (MINLP) problem and can be rewritten as a single-level MINLP problem, where each nonlinear constraint corresponds to a hypograph of a multiple ratio function characterizing the leader's market share for a fixed follower's location choice. By establishing the submodularity of the multiple ratio functions, we characterize the mixed 0-1 set induced by each hypograph using submodular inequalities and extend a state-of-the-art branch-and-cut (B&C) algorithm to the considered SCFLP. To address the challenge of poor linear programming (LP) relaxation of the underlying formulation, we develop two new mixed integer linear programming (MILP) formulations for the SCFLP as well as efficient B&C algorithms based on them. The first MILP formulation is based on a class of improved submodular inequalities, which include the classic submodular inequalities as special cases, and together with the trivial inequalities characterize the convex hull of the mixed 0-1 set. The second one is an extended formulation of the first one that provides the same LP relaxation bound. We also develop efficient algorithms for the separations of the exponential families of the inequalities in the MILP formulations. Extensive computational experiments show that the proposed B&C algorithms significantly outperform an adapted state-of-the-art B&C algorithm and a sophisticated heuristic algorithm in the literature. Moreover, the proposed B&C algorithms can find optimal solutions for SCFLP instances with up to 1000 customers and facilities within a two-hour time limit.

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arXiv2025

A Dynamic Relaxation Framework for Global Solution of ACOPF

Solving the Alternating Current Optimal Power Flow (AC OPF) problem to global optimality remains challenging due to its nonconvex quadratic constraints. In this paper, we present a unified framework that combines static piecewise relaxations with dynamic cut-generation mechanism to systematically tighten the classic Second-Order Cone Programming (SOCP) relaxation to arbitrarily small conic violation, thus enabling the recovery of globally optimal solutions. Two static formulations, Pyramidal Relaxation (PR) and Quasi-Pyramidal Relaxation (QPR), are introduced to tighten each branch-flow second-order cone via a finite union of wedges, providing controllable accuracy. Their dynamic counterparts, Dynamic PR (DPR) and Dynamic QPR (DQPR), embed on-the-fly cut generation within a branch-and-cut solver to improve scalability. Convergence is further accelerated through warm starts and a lightweight local-search post-processing. Extensive experiments on benchmarks demonstrate effective elimination of conic violations and flexible trade-offs between solution accuracy and runtime. Practical guidelines are derived for selecting appropriate variants based on network size and accuracy requirements.

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arXiv2025

A Newton Augmented Lagrangian Method for Symmetric Cone Programming with Complexity Analysis

Symmetric cone programming covers a broad class of convex optimization problems, including linear programming, second-order cone programming, and semidefinite programming. Although the augmented Lagrangian method (ALM) is well-suited for large-scale problems, its subproblems are often not twice continuously differentiable, preventing the direct use of classical Newton methods. To address this issue, we observe that barrier functions used in interior-point methods (IPMs) naturally serve as effective smoothing terms to alleviate such nonsmoothness. By combining the strengths of ALM and IPMs, we construct a novel augmented Lagrangian function and subsequently develop a Newton augmented Lagrangian (NAL) method. By leveraging the self-concordance property of the barrier function, the proposed method is shown to achieve an $\mathcal{O}(1/{\epsilon})$ complexity bound. In addition, a spectral analysis reveals that the condition numbers of the Schur complement matrices arising in the NAL method are of order $\mathcal{O}(1/{\mu})$, which is better than the $\mathcal{O}(1/{\mu^2})$ order of classical IPMs. This improvement is further illustrated by a heatmap of condition numbers. Numerical experiments conducted on standard benchmarks indicate that the NAL method exhibits significant performance improvements compared to several existing methods.

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arXiv2025

Spectral-Spatial Extraction through Layered Tensor Decomposition for Hyperspectral Anomaly Detection

Low rank tensor representation (LRTR) methods are very useful for hyperspectral anomaly detection (HAD). To overcome the limitations that they often overlook spectral anomaly and rely on large-scale matrix singular value decomposition, we first apply non-negative matrix factorization (NMF) to alleviate spectral dimensionality redundancy and extract spectral anomaly and then employ LRTR to extract spatial anomaly while mitigating spatial redundancy, yielding a highly efffcient layered tensor decomposition (LTD) framework for HAD. An iterative algorithm based on proximal alternating minimization is developed to solve the proposed LTD model, with convergence guarantees provided. Moreover, we introduce a rank reduction strategy with validation mechanism that adaptively reduces data size while preventing excessive reduction. Theoretically, we rigorously establish the equivalence between the tensor tubal rank and tensor group sparsity regularization (TGSR) and, under mild conditions, demonstrate that the relaxed formulation of TGSR shares the same global minimizers and optimal values as its original counterpart. Experimental results on the Airport-Beach-Urban and MVTec datasets demonstrate that our approach outperforms state-of-the-art methods in the HAD task.

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arXiv2025

Triangle Steepest Descent: A Geometry-Based Gradient Algorithm with Guaranteed R-Linear Convergence

Gradient methods are among the simplest yet most widely used algorithms for unconstrained optimization. Motivated by a geometric property of the steepest descent (SD) method that can alleviate the zigzag behavior in quadratic problems, we develop a new gradient variant called the Triangle Steepest Descent (TSD) method. The TSD method introduces a cycle parameter $j$ that governs the periodic combination of past search directions, providing a geometry-driven mechanism to enhance convergence. To the best of our knowledge, TSD is the first formally established geometry-based gradient scheme since Akaike (1959). We prove that TSD is at least R-linearly convergent for strongly convex quadratic problems and demonstrate through extensive numerical experiments that it exhibits superlinear behavior, outperforming the Barzilai-Borwein (BB) method and monotone Dai-Yuan gradient method (DY) in quadratic cases. These results suggest that incorporating geometric information into gradient directions offers a promising avenue for developing efficient optimization algorithms.

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