Related papers: Rotation Averaging and Strong Duality
Rotation Averaging is a non-convex optimization problem that determines orientations of a collection of cameras from their images of a 3D scene. The problem has been studied using a variety of distances and robustifiers. The intrinsic (or…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
Consider the joint beamforming and quantization problem in the cooperative cellular network, where multiple relay-like base stations (BSs) connected to the central processor (CP) via rate-limited fronthaul links cooperatively serve the…
Multiple rotation averaging is an essential task for structure from motion, mapping, and robot navigation. The task is to estimate the absolute orientations of several cameras given some of their noisy relative orientation measurements. The…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…
Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
We propose a duality scheme for solving constrained nonsmooth and nonconvex optimization problems in a reflexive Banach space. We establish strong duality for a very general type of augmented Lagrangian, in which we assume a less…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…