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Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…
Modern state estimation is often formulated as an optimization problem and solved using efficient local search methods. These methods at best guarantee convergence to local minima, but, in some cases, global optimality can also be…
Factor graph optimization serves as a fundamental framework for robotic perception, enabling applications such as pose estimation, simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and situational awareness.…
We consider the maximum-a-posteriori inference problem in discrete graphical models and study solvers based on the dual block-coordinate ascent rule. We map all existing solvers in a single framework, allowing for a better understanding of…
Motivated by recent work of Renegar, we present new computational methods and associated computational guarantees for solving convex optimization problems using first-order methods. Our problem of interest is the general convex optimization…
The use of momentum in stochastic optimization algorithms has shown empirical success across a range of machine learning tasks. Recently, a new class of stochastic momentum algorithms has emerged within the Linear Minimization Oracle (LMO)…
Integer programming with block structures has received considerable attention recently and is widely used in many practical applications such as train timetabling and vehicle routing problems. It is known to be NP-hard due to the presence…
The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and…
In this paper, we study the Multi-Objective Bi-Level Optimization (MOBLO) problem, where the upper-level subproblem is a multi-objective optimization problem and the lower-level subproblem is for scalar optimization. Existing gradient-based…
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…
Complex-variable matrix optimization problems (CMOPs) in Frobenius norm emerge in many areas of applied mathematics and engineering applications. In this letter, we focus on solving CMOPs by iterative methods. For unconstrained CMOPs, we…
Planes are generally used in 3D reconstruction for depth sensors, such as RGB-D cameras and LiDARs. This paper focuses on the problem of estimating the optimal planes and sensor poses to minimize the point-to-plane distance. The resulting…
Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…
In this paper, we consider the problem of distributed pose graph optimization (PGO) that has extensive applications in multi-robot simultaneous localization and mapping (SLAM). We propose majorization minimization methods to distributed PGO…
This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…
Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…