Related papers: A Modified Proximal Bundle Method Under A Frank-Wo…
We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is…
In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane…
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
A core component of all Structure from Motion (SfM) approaches is bundle adjustment. As the latter is a computational bottleneck for larger blocks, parallel bundle adjustment has become an active area of research. Particularly,…
Most methods for Bundle Adjustment (BA) in computer vision are either centralized or operate incrementally. This leads to poor scaling and affects the quality of solution as the number of images grows in large scale structure from motion…
We propose the novel p-branch-and-bound method for solving two-stage stochastic programming problems whose deterministic equivalents are represented by non-convex mixed-integer quadratically constrained quadratic programming (MIQCQP)…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides…
Bundle adjustment (BA) with parallax angle based feature parameterization has been shown to have superior performance over BA using inverse depth or XYZ feature forms. In this paper, we propose an improved version of the parallax BA…
The Poisson multi-Bernoulli mixture (PMBM) is a multi-object conjugate prior for the closed-form Bayes random finite sets filter. The extended object PMBM filter provides a closed-form solution for multiple extended object filtering with…
In this paper we propose a proximal algorithm for minimizing an objective function of two block variables consisting of three terms: 1) a smooth function, 2) a nonsmooth function which is a composition between a strictly increasing,…
In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…