Searcharxiv⌕ Search

arXiv subjects

Yacine Mokhtari

Publications and source records attributed to Yacine Mokhtari.

6 recordsLinked to original sources
arXiv2026

TenderKG

Public procurement represents a major economic activity, where public institutions allocate contracts to companies through competitive tendering processes. Despite its importance, this domain remains underexplored by recommender systems, largely due to the lack of publicly available datasets capturing its complexity. In this paper, we introduce TenderKG, a large-scale knowledge graph dataset constructed from French public procurement data covering the period 2021--2023. The dataset models the procurement ecosystem through heterogeneous entities, including companies, tenders, lots, and domain-specific taxonomies of work domains, connected via rich semantic and structural relations. A key specificity of this setting is that only the awarded companies are visible, resulting in sparse explicit signals of awarded interactions. To overcome this limitation, TenderKG integrates extensive side information on the actors in the French tender market and the tenders, including textual descriptions, hierarchical classifications, and geographical features, enabling the study of knowledge-aware recommendation in a highly constrained and competitive environment. We provide detailed statistics and analyses of the dataset, highlighting its structural properties, sparsity patterns, and domain-specific characteristics. We believe TenderKG opens new research directions in bidder recommendation, knowledge graph-based recommendation, competition-aware matching, and provides a valuable benchmark for evaluating methods in real-world, high-stakes decision-making scenarios.

cs.IR↗
arXiv2026

Velocity Reconstruction from Flow-Induced Magnetic Fields

We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the evolution of the magnetic perturbation $\boldsymbol{b}$ is governed by the linearized induction equation. We analyze the system on both the entire space $Ω= \mathbb{R}^d$ and a periodic domain $Ω= \prod_{i=1}^d [0, L_i)$, which models a homogeneous medium with side lengths $L_i > 0$. We analyze this problem by decomposing it into the injectivity of a parabolic forward map and the solvability of a divergence-free transport sub-problem. On the whole space $\mathbb{R}^d$, we show that the transport sub-problem is well-posed when data is prescribed on a non-characteristic hypersurface transverse to $\mathbf{F}$. On the torus, we establish a sharp uniqueness criterion based on the rational dependence of the ratios $\{F_i/L_i\}_{i=1}^d$ between the background-field components and the corresponding domain periods. Furthermore, we show that for the reconstructed velocity to belong to $L^2$, a sufficient condition is that the background field must satisfy a Diophantine condition. The proof combines injectivity of the parabolic forward map with uniqueness for a steady transport equation along $\mathbf{F}$.

math.AP↗
arXiv2026

A Heuristic Alternating Direction Method of Multipliers Framework for Distributed and Centralized Tree-Constrained Optimization: Applications to Hop-Constrained Spanning Tree Multicommodity Flow Design

This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted arborescence constraints. We address the combinatorial complexity by introducing a continuous relaxation of the binary variables and enforcing agreement through an augmented Lagrangian formulation. The algorithms alternate between solving a convex continuous subproblem and projecting onto the tree-feasible set, reducing to a Minimum Spanning Tree or Minimum Weight Rooted Arborescence problem, both solvable in polynomial time. The distributed algorithm enables agents to cooperate via local communication, enhancing scalability and robustness. We apply the framework to multicommodity flow design with hop-constrained spanning trees. Numerical experiments demonstrate that our methods yield high-quality feasible solutions in many cases, achieving near-optimal performance.

math.OC↗
arXiv2025

Distributed ADMM Approach for the Power Distribution Network Reconfiguration

The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring radial topology. The growing use of renewable energy and the complexity of managing modern power grids make solving the reconfiguration problem crucial. Distributed algorithms help optimize grid configurations, ensuring efficient adaptation to changing conditions and better utilization of renewable energy sources. This paper introduces a distributed algorithm designed to tackle the problem of power distribution network reconfiguration with a radiality constraint. This algorithm relies on ADMM (Alternating Direction Method of Multipliers), where each agent progressively updates its estimation based on the information exchanged with neighboring agents. We show that every agent is required to solve a linearly constrained convex quadratic programming problem and a Minimum Weight Rooted Arborescence Problem (MWRAP) with local weights during each iteration. Through numerical experiments, we demonstrate the performance of the proposed algorithm in various scenarios, including its application to a 33-bus test system and a real-world network.

eess.SY↗
arXiv2025

An ADMM-Based Approach to Quadratically-Regularized Distributed Optimal Transport on Graphs

Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal transport problem on directed, strongly connected graphs, unlike previous approaches which were limited to bipartite graphs. Our algorithm incorporates quadratic regularization and guarantees convergence using the Alternating Direction Method of Multipliers (ADMM). Notably, it proves convergence not only with quadratic regularization but also in cases without it, whereas earlier works required strictly convex objective functions. In this approach, nodes are treated as agents that collaborate through local interactions to optimize the total transportation cost, relying only on information from their neighbors. Through numerical experiments, we show how quadratic regularization affects both convergence behavior and solution sparsity under different graph structures. Additionally, we provide a practical example that highlights the algorithm's robustness through its ability to adjust to topological changes in the graph.

math.OC↗