Related papers: Building Rome with Convex Optimization
We study convergence rates of the classic proximal bundle method for a variety of nonsmooth convex optimization problems. We show that, without any modification, this algorithm adapts to converge faster in the presence of smoothness or a…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving optimization problems with nonsmooth components. In this paper, we conduct a theoretical investigation of a modified proximal bundle…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of…
This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Functional complexity bounds for…
Bundle adjustment (BA) is a technique for refining sensor orientations of satellite images, while adjustment accuracy is correlated with feature matching results. Feature match-ing often contains high uncertainties in weak/repeat textures,…
Accurate 3D reconstruction from unstructured image collections is a key requirement in applications such as robotics, mapping, and scene understanding. While global Structure from Motion (SfM) techniques rely on full image connectivity and…
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees.…
Augmented Lagrangian Method (ALM) combined with Burer-Monteiro (BM) factorization, dubbed ALM-BM, offers a powerful approach for solving large-scale low-rank semidefinite programs (SDPs). Despite its empirical success, the theoretical…
We consider the problem of simultaneously estimating a dense depth map and camera pose for a large set of images of an indoor scene. While classical SfM pipelines rely on a two-step approach where cameras are first estimated using a bundle…
This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…
Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
Prediction models are typically optimized independently from decision optimization. A smart predict then optimize (SPO) framework optimizes prediction models to minimize downstream decision regret. In this paper we present dboost, the first…
We propose a Langevin diffusion-based algorithm for non-convex optimization and sampling on a product manifold of spheres. Under a logarithmic Sobolev inequality, we establish a guarantee for finite iteration convergence to the Gibbs…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
This paper presents an efficient algorithm for the least-squares problem using the point-to-plane cost, which aims to jointly optimize depth sensor poses and plane parameters for 3D reconstruction. We call this least-squares problem…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on a model that involves the convex hull of previously…
In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…