相关论文: Fast globally optimal Truncated Least Squares poin…

In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular semidefinite relaxation of K-means clustering which…

In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…

Point cloud registration plays a crucial role in various fields, including robotics, computer graphics, and medical imaging. This process involves determining spatial relationships between different sets of points, typically within a 3D…

We address the problem of recovering a signal (up to global phase) from its short-time Fourier transform (STFT) magnitude measurements. This problem arises in several applications, including optical imaging and speech processing. In this…

In this paper we study the relationship between the optimal value of a homogeneous quadratic optimization problem and that of its Semidefinite Programming (SDP) relaxation. We consider two quadratic optimization models: (1) $\min \{x^* C x…

Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…

We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…

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…

We propose a method for speeding up a 3D point cloud registration through a cascading feature extraction. The current approach with the highest accuracy is realized by iteratively executing feature extraction and registration using deep…

We consider the problem of rigid registration, where we wish to jointly register multiple point sets via rigid transforms. This arises in applications such as sensor network localization, multiview registration, and protein structure…

Constructing precise global maps is a key task in robotics and is required for localization, surveying, monitoring, or constructing digital twins. To build accurate maps, data from mobile 3D LiDAR sensors is often used. Mapping requires…

In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

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…

Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least-squares…

Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…

This paper proposes a sequential convex relaxation method for obtaining feasible and near-globally optimal solutions for unit commitment (UC) with AC transmission constraints. First, we develop a second-order cone programming (SOCP)…

This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…