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Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
The Bayesian approach to clustering is often appreciated for its ability to provide uncertainty in the partition structure. However, summarizing the posterior distribution over the clustering structure can be challenging, due the discrete,…
Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller…
Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are…
Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…
We present a method to solve the problem of Rashba spin-orbit coupling in semiconductor quantum dots, within the context of quasi-exactly solvable spectral problems. We show that the problem possesses a hidden osp(2,2) superalgebra. We…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using…
He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in…
In recent years, there has been remarkable progress in the development of so-called certifiable perception methods, which leverage semidefinite, convex relaxations to find global optima of perception problems in robotics. However, many of…
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…
This paper studies the integrated spacecraft routing and trajectory optimization problem for satellite servicing missions involving partial en-route propellant replenishment. Unlike terrestrial routing problems, spacecraft operate in a…
This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\ell_1$ unit ball (QPL1). It dominates the state-of-the-art…
In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…