arXiv subjects

Akang Wang

Publications and source records attributed to Akang Wang.

At least 19 recordsLinked to original sources

arXiv2026

Congruence Decomposition with Neural Block Solvers for Large-Scale PCI Assignment

Physical Cell Identity (PCI) assignment is essential for interference management in dense 5G networks. As cellular networks scale, PCI reuse becomes unavoidable, which may cause collisions, confusions, and multiple forms of modular interference. Jointly mitigating these effects gives rise to a large-scale, multi-objective combinatorial optimization problem that is difficult to solve efficiently at practical network scales. In this work, we propose a congruence decomposition framework with neural block solvers for large-scale PCI assignment. The proposed decomposition exploits the arithmetic structure of PCI values to decouple multiple modular interference objectives into a collection of blockwise Min-$k$-Partition subproblems, followed by a graph coloring procedure to resolve PCI conflicts. For the resulting NP-hard Min-$k$-Partition subproblems, we develop neural block solvers by parameterizing their relaxed quadratic formulations with graph neural networks, enabling efficient optimization at large scales. Discrete assignments are recovered through conditional expectation rounding with theoretical guarantees. Experiments on synthetic cellular graphs and real-world 5G networks show that the proposed method consistently outperforms existing modular-interference-aware baselines in modular interference reduction, conflict elimination, and computational efficiency.

cs.LG↗

arXiv2026

[CLS] is Not Enough: Multi-Label Recognition via Patch-Level Inference and Adaptive Aggregation

Vision-Language Models such as CLIP exhibit strong zero-shot recognition capability by aligning images with textual concepts, yet they often underperform on multi-label recognition where multiple objects co-exist. A key bottleneck is that the [CLS] token, as a single global visual representation, is insufficient to faithfully encode diverse targets with varying scales, contexts, and co-occurrence patterns. To address this limitation, we present a new multi-label image recognition framework, termed PIAA, which formulates prediction as Patch-level Inference followed by Adaptive Aggregation. Specifically, we first enhance patch-wise predictions from two complementary perspectives: (i) mitigating semantic entanglement in the visual encoder to obtain more discriminative patch representations, and (ii) learning an unsupervised visual classifier to narrow the vision-language modality gap. We then introduce an adaptive aggregation module that consolidates patch-level scores into the final multi-label prediction. Notably, the entire pipeline is fully training-free, requiring no gradient updates or parameter fine-tuning. Experiments show that our method achieves strong improvements with minimal extra computation, exceeding a 6% mAP gain on the challenging NUS-WIDE benchmark over representative baselines. Code is available at https://github.com/akang-wang/PIAA.

cs.CV↗

arXiv2026

Promoting Fair Online Resource Allocation with Indivisible Units

Allocating scarce, indivisible resources to diverse groups under uncertainty is a central challenge in operations research, where efficiency-focused methods often underserve marginalized populations. We study the Fair Online Resource Allocation with Indivisible Units (FORA-IU) problem, in which an unpredictable sequence of demands must be served from a strictly fixed inventory, and ask what fairness guarantees are achievable under different distributional and structural assumptions. We adopt a fairness criterion based on the expected filling ratio (FE-FR-beta), which balances each group's expected allocation against its expected demand and priority weight. We design online policies that calibrate acceptance probabilities to the remaining budget, analyze both arbitrary time-varying and stationary arrivals, introduce the Random Cyclic Blocks (RCB) algorithm tailored to the stationary case, and study the effect of restricting policies to all-or-nothing allocations. For arbitrary time-varying arrivals, our policy achieves the optimal universal fairness guarantee of 1/(1+R_beta), where R_beta denotes the priority-weighted system load. For time-invariant arrivals, RCB achieves the exact finite-horizon guarantee [1-(1-R_beta/T)^T]/R_beta, which is at least (1-e^{-R_beta})/R_beta and is also tight. We further show that all-or-nothing allocation policies cannot match these guarantees. These findings demonstrate that distributional stationarity strictly improves the fairness frontier, and that partial fulfillment is a necessary condition for attaining optimal fairness in online indivisible resource allocation.

math.OC↗

arXiv2025

An Accelerated Mixed Weighted-Unweighted MMSE Approach for MU-MIMO Beamforming

Precoding design based on weighted sum-rate (WSR) maximization is a fundamental problem in downlink multi-user multiple-input multiple-output (MU-MIMO) systems. While the weighted minimum mean-square error (WMMSE) algorithm is a standard solution, its high computational complexity--cubic in the number of base station antennas due to matrix inversions--hinders its application in latency-sensitive scenarios. To address this limitation, we propose a highly parallel algorithm based on a block coordinate descent framework. Our key innovation lies in updating the precoding matrix via block coordinate gradient descent, which avoids matrix inversions and relies solely on matrix multiplications, making it exceptionally amenable to GPU acceleration. We prove that the proposed algorithm converges to a stationary point of the WSR maximization problem. Furthermore, we introduce a two-stage warm-start strategy grounded in the sum mean-square error (MSE) minimization problem to accelerate convergence. We refer to our method as the Accelerated Mixed weighted-unweighted sum-MSE minimization (A-MMMSE) algorithm. Simulation results demonstrate that A-MMMSE matches the WSR performance of both conventional WMMSE and its enhanced variant, reduced-WMMSE, while achieving a substantial reduction in computational time across diverse system configurations.

eess.SP↗

arXiv2025

Successive Fixing for Large-Scale SCUC Using First-Order Methods

Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within branch-and-cut. Conventional simplex and barrier methods become computationally prohibitive at this scale due to their reliance on expensive matrix factorizations. While matrix-free first-order methods present a promising alternative, their tendency to converge to non-vertex solutions renders them incompatible with standard branch-and-cut procedures. To bridge this gap, we propose a successive fixing framework that leverages a customized GPU-accelerated first-order LP solver to guide a logic-driven variable-fixing strategy. Each iteration produces a reduced Mixed-Integer Linear Programming (MILP) problem, which is subsequently tightened via presolving. This iterative cycle of relaxation, fixing, and presolving progressively reduces problem complexity, producing a highly tractable final MILP model. When evaluated on public benchmarks exceeding 13,000 buses, our approach achieves a tenfold speedup over state-of-the-art methods without compromising solution quality.

math.OC↗

arXiv2025

QuadEnhancer: Leveraging Quadratic Transformations to Enhance Deep Neural Networks

The combination of linear transformations and non-linear activation functions forms the foundation of most modern deep neural networks, enabling them to approximate highly complex functions. This paper explores the introduction of quadratic transformations to further increase nonlinearity in neural networks, with the aim of enhancing the performance of existing architectures. To reduce parameter complexity and computational complexity, we propose a lightweight quadratic enhancer that uses low-rankness, weight sharing, and sparsification techniques. For a fixed architecture, the proposed approach introduces quadratic interactions between features at every layer, while only adding negligible amounts of additional model parameters and forward computations. We conduct a set of proof-of-concept experiments for the proposed method across three tasks: image classification, text classification, and fine-tuning large-language models. In all tasks, the proposed approach demonstrates clear and substantial performance gains.

cs.LG↗

arXiv2025

Smoothing Binary Optimization: A Primal-Dual Perspective

Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with large-scale instances. In this work, we introduce a novel primal-dual framework that reformulates unconstrained binary optimization as a continuous minimax problem, satisfying a strong max-min property. This reformulation effectively smooths the discrete problem, enabling the application of efficient gradient-based methods. We propose a simultaneous gradient descent-ascent algorithm that is highly parallelizable on GPUs and provably converges to a near-optimal solution in linear time. Extensive experiments on large-scale problems--including Max-Cut, MaxSAT, and Maximum Independent Set with up to 50,000 variables--demonstrate that our method identifies high-quality solutions within seconds, significantly outperforming state-of-the-art alternatives.

math.OC↗

arXiv2025

Solving Quadratic Programs via Deep Unrolled Douglas-Rachford Splitting

Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its robust convergence properties. Concurrently, the emerging field of Learning-to-Optimize offers promising avenues for enhancing algorithmic performance, with algorithm unrolling receiving considerable attention due to its computational efficiency and interpretability. In this work, we propose an approach that unrolls a modified DR splitting algorithm to efficiently learn solutions for convex QPs. Specifically, we introduce a tailored DR splitting algorithm that replaces the computationally expensive linear system-solving step with a simplified gradient-based update, while retaining convergence guarantees. Consequently, we unroll the resulting DR splitting method and present a well-crafted neural network architecture to predict QP solutions. Our method achieves up to 50% reductions in iteration counts and 40% in solve time across benchmarks on both synthetic and real-world QP datasets, demonstrating its scalability and superior performance in enhancing computational efficiency across varying sizes.

math.OC↗

arXiv2025

Relax-and-Cut for Temporal SCUC Decomposition

The Security-Constrained Unit Commitment (SCUC) problem presents formidable computational challenges due to its combinatorial complexity, large-scale network dimensions, and numerous security constraints. While conventional temporal decomposition methods achieve computational tractability through fixed short-term time windows, this limited look-ahead capability often results in suboptimal, myopic solutions. We propose an innovative relax-and-cut framework that alleviates these limitations through two key innovations. First, our enhanced temporal decomposition strategy maintains integer variables for immediate unit commitment decisions while relaxing integrality constraints for future time periods, thereby extending the optimization horizon without compromising tractability. Second, we develop a dynamic cutting-plane mechanism that selectively incorporates N-1 contingency constraints during the branch-and-cut process, avoiding the computational burden of complete upfront enumeration. The framework optionally employs a Relaxation-Induced Neighborhood Search procedure for additional solution refinement when computational resources permit. Comprehensive numerical experiments demonstrate the effectiveness of our approach on large-scale systems up to 13,000 buses. The proposed method can achieve optimality gaps below 1% while requiring only 20% of the computation time of monolithic Gurobi solutions. Compared to existing decomposition approaches, our framework provides superior performance, simultaneously reducing primal gaps by 60% and doubling solution speed. These significant improvements make our method particularly well-suited for practical SCUC implementations where both solution quality and computational efficiency are crucial.

math.OC↗

arXiv2025

A Learning-Based Inexact ADMM for Solving Quadratic Programs

Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has emerged as a preferred first-order approach due to its iteration efficiency - exemplified by the state-of-the-art OSQP solver. Machine learning-enhanced optimization algorithms have recently demonstrated significant success in speeding up the solving process. This work introduces a neural-accelerated ADMM variant that replaces exact subproblem solutions with learned approximations through a parameter-efficient Long Short-Term Memory (LSTM) network. We derive convergence guarantees within the inexact ADMM formalism, establishing that our learning-augmented method maintains primal-dual convergence while satisfying residual thresholds. Extensive experimental results demonstrate that our approach achieves superior solution accuracy compared to existing learning-based methods while delivering significant computational speedups of up to $7\times$, $28\times$, and $22\times$ over Gurobi, SCS, and OSQP, respectively. Furthermore, the proposed method outperforms other learning-to-optimize methods in terms of solution quality. Detailed performance analysis confirms near-perfect compliance with the theoretical assumptions, consequently ensuring algorithm convergence.

math.OC↗

arXiv2025

When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approach

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a significant challenge arises when applying GNNs to ILPs with symmetry: classic GNN architectures struggle to differentiate between symmetric variables, which limits their predictive accuracy. In this work, we investigate the properties of permutation equivariance and invariance in GNNs, particularly in relation to the inherent symmetry of ILP formulations. We reveal that the interaction between these two factors contributes to the difficulty of distinguishing between symmetric variables. To address this challenge, we explore the potential of feature augmentation and propose several guiding principles for constructing augmented features. Building on these principles, we develop an orbit-based augmentation scheme that first groups symmetric variables and then samples augmented features for each group from a discrete uniform distribution. Empirical results demonstrate that our proposed approach significantly enhances both training efficiency and predictive performance.

cs.LG↗

arXiv2024

Parallel Graver Basis Extraction for Nonlinear Integer Optimization

The augmentation scheme provides a nontraditional approach to nonlinear integer programming by iteratively refining incumbent solutions along objective-improving directions from the Graver basis. Its main computational bottleneck, however, lies in the practical difficulty of accessing such directions. To address this challenge, we develop a massively parallel heuristic for approximating Graver basis, extracting promising directions by optimizing nonconvex continuous problems using parallelizable first-order methods. Experiments on QPLIB and MINLPLib instances show that our method achieves comparable performance to advanced solvers.

math.OC↗

arXiv2024

Mixed-Integer Linear Optimization via Learning-Based Two-Layer Large Neighborhood Search

Mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions within specific neighborhoods. Recent advancements have integrated machine learning techniques into LNS to guide the construction of these neighborhoods effectively. However, for large-scale MILPs, the search step in LNS becomes a computational bottleneck, relying on off-the-shelf solvers to optimize auxiliary MILPs of substantial size. To address this challenge, we introduce a two-layer LNS (TLNS) approach that employs LNS to solve both the original MILP and its auxiliary MILPs, necessitating the optimization of only small-sized MILPs using off-the-shelf solvers. Additionally, we incorporate a lightweight graph transformer model to inform neighborhood design. We conduct extensive computational experiments using public benchmarks. The results indicate that our learning-based TLNS approach achieves remarkable performance gains--up to 66% and 96% over LNS and state-of-the-art MILP solvers, respectively.

math.OC↗

arXiv2024

ROS: A GNN-based Relax-Optimize-and-Sample Framework for Max-k-Cut Problems

The Max-k-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic NP-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-k-Cut, they often lack guarantees of equivalence between the solutions of the original problem and its relaxation. To address this issue, we introduce the Relax-Optimize-and-Sample (ROS) framework. In particular, we begin by relaxing the discrete constraints to the continuous probability simplex form. Next, we pre-train and fine-tune a graph neural network model to efficiently optimize the relaxed problem. Subsequently, we propose a sampling-based construction algorithm to map the continuous solution back to a high-quality Max-k-Cut solution. By integrating geometric landscape analysis with statistical theory, we establish the consistency of function values between the continuous solution and its mapped counterpart. Extensive experimental results on random regular graphs and the Gset benchmark demonstrate that the proposed ROS framework effectively scales to large instances with up to 20000 nodes in just a few seconds, outperforming state-of-the-art algorithms. Furthermore, ROS exhibits strong generalization capabilities across both in-distribution and out-of-distribution instances, underscoring its effectiveness for large-scale optimization tasks.

math.OC↗

arXiv2024

An Efficient Unsupervised Framework for Convex Quadratic Programs via Deep Unrolling

Quadratic programs (QPs) arise in various domains such as machine learning, finance, and control. Recently, learning-enhanced primal-dual hybrid gradient (PDHG) methods have shown great potential in addressing large-scale linear programs; however, this approach has not been extended to QPs. In this work, we focus on unrolling "PDQP", a PDHG algorithm specialized for convex QPs. Specifically, we propose a neural network model called "PDQP-net" to learn optimal QP solutions. Theoretically, we demonstrate that a PDQP-net of polynomial size can align with the PDQP algorithm, returning optimal primal-dual solution pairs. We propose an unsupervised method that incorporates KKT conditions into the loss function. Unlike the standard learning-to-optimize framework that requires optimization solutions generated by solvers, our unsupervised method adjusts the network weights directly from the evaluation of the primal-dual gap. This method has two benefits over supervised learning: first, it helps generate better primal-dual gap since the primal-dual gap is in the objective function; second, it does not require solvers. We show that PDQP-net trained in this unsupervised manner can effectively approximate optimal QP solutions. Extensive numerical experiments confirm our findings, indicating that using PDQP-net predictions to warm-start PDQP can achieve up to 45% acceleration on QP instances. Moreover, it achieves 14% to 31% acceleration on out-of-distribution instances.

math.OC↗

arXiv2024

On Representing Convex Quadratically Constrained Quadratic Programs via Graph Neural Networks

Convex quadratically constrained quadratic programs (QCQPs) involve finding a solution within a convex feasible region defined by quadratic constraints while minimizing a convex quadratic objective function. These problems arise in various industrial applications, including power systems and signal processing. Traditional methods for solving convex QCQPs primarily rely on matrix factorization, which quickly becomes computationally prohibitive as the problem size increases. Recently, graph neural networks (GNNs) have gained attention for their potential in representing and solving various optimization problems such as linear programs and linearly constrained quadratic programs. In this work, we investigate the representation power of GNNs in the context of QCQP tasks. Specifically, we propose a new tripartite graph representation for general convex QCQPs and properly associate it with message-passing GNNs. We demonstrate that there exist GNNs capable of reliably representing key properties of convex QCQPs, including feasibility, optimal value, and optimal solution. Our result deepens the understanding of the connection between QCQPs and GNNs, paving the way for future machine learning approaches to efficiently solve QCQPs.

math.OC↗

arXiv2024

IPM-LSTM: A Learning-Based Interior Point Method for Solving Nonlinear Programs

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM). The most computationally expensive procedure in IPMs is to solve systems of linear equations via matrix factorization. Recently, machine learning techniques have been adopted to expedite classic optimization algorithms. In this work, we propose using Long Short-Term Memory (LSTM) neural networks to approximate the solution of linear systems and integrate this approximating step into an IPM. The resulting approximate NLP solution is then utilized to warm-start an interior point solver. Experiments on various types of NLPs, including Quadratic Programs and Quadratically Constrained Quadratic Programs, show that our approach can significantly accelerate NLP solving, reducing iterations by up to 60% and solution time by up to 70% compared to the default solver.

math.OC↗

arXiv2024

SymILO: A Symmetry-Aware Learning Framework for Integer Linear Optimization

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods -- achieving $50.3\%$, $66.5\%$, and $45.4\%$ average improvements, respectively.

math.OC↗