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Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide…

Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…

The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing global optimality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF)…

We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large…

Rigid Point Cloud Registration (PCR) algorithms aim to estimate the 6-DOF relative motion between two point clouds, which is important in various fields, including autonomous driving. Recent years have seen a significant improvement in…

We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…

Global registration is a fundamental task that estimates the relative pose between two viewpoints of 3D point clouds. However, there are two issues that degrade the performance of global registration in LiDAR SLAM: one is the sparsity issue…

Point cloud registration sits at the core of many important and challenging 3D perception problems including autonomous navigation, SLAM, object/scene recognition, and augmented reality. In this paper, we present a new registration…

This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…

This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…

A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…

In this paper, we propose a coarse-to-fine integration solution inspired by the classical ICP algorithm, to pairwise 3D point cloud registration with two improvements of hybrid metric spaces (eg, BSC feature and Euclidean geometry spaces)…

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific…

We provide a dynamical perspective on the classical problem of 3D point cloud registration with correspondences. A point cloud is considered as a rigid body consisting of particles. The problem of registering two point clouds is formulated…

We propose semidefinite trajectory optimization (STROM), a framework that computes fast and certifiably optimal solutions for nonconvex trajectory optimization problems defined by polynomial objectives and constraints. STROM employs sparse…

We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…

Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite…

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…

In this paper, we investigate the optimal $\mathcal{H}_2$ model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine…