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Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…

We show that (i) any constrained polynomial optimization problem (POP) has an equivalent formulation on a variety contained in an Euclidean sphere and (ii) the resulting semidefinite relaxations in the moment-SOS hierarchy have the constant…

We present a fast algorithm to solve nesting problems based on a semi-discrete representation of both the 2D non-convex pieces and the strip. The pieces and the strip are represented by a set of equidistant vertical line segments. The…

This paper deals with the non-convex power system state estimation (PSSE) problem, which plays a central role in the monitoring and operation of electric power networks. Given a set of noisy measurements, PSSE aims at estimating the vector…

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that,…

In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations for a general polynomial optimization problem (POP). However, due to…

Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…

We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…

Loop closure detection (LCD) is an indispensable part of simultaneous localization and mapping systems (SLAM); it enables robots to produce a consistent map by recognizing previously visited places. When robots operate over extended…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge…

Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…

We present the first algorithm to efficiently compute certifiably optimal solutions to range-aided simultaneous localization and mapping (RA-SLAM) problems. Robotic navigation systems increasingly incorporate point-to-point ranging sensors,…

Large Language Models (LLMs) have demonstrated strong capabilities in various natural language processing tasks; however, their application to graph-related problems remains limited, primarily due to scalability constraints and the absence…

In this paper, we consider signal detection algorithms in a multiple-input multiple-output (MIMO) decode-forward (DF) relay channel with one source, one relay, and one destination. The existing suboptimal near maximum likelihood (NML)…

Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…

The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…

Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study conditions under which the standard semidefinite program (SDP) relaxation of a…

Software Defined Networking (SDN) is a recent paradigm in telecommunication networks that disentangles data and control planes and brings more flexibility and efficiency to the network as a result. The Controller Placement (CP) problem in…

Bilevel hyperparameter optimization has received growing attention thanks to the fast development of machine learning. Due to the tremendous size of data sets, the scale of bilevel hyperparameter optimization problem could be extremely…