Related papers: Global Nonconvex Optimization with Integer Variabl…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern…
We investigate optimization models for the purpose of computational redistricting. Our focus is on nonconvex objectives for estimating expected Black Representatives and Political Representation. The objectives are a composition of a ratio…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
In this paper, we propose a novel locally statistical active contour model (LACM) based on Aubert-Aujol (AA) denoising model and variational level set method, which can be used for SAR images segmentation with intensity inhomogeneity. Then…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
The globally optimal robust adaptive beamforming (RAB) solution is studied for worst-case signal-to-interference-plus-noise ratio (SINR) maximization (the maximin SINR problem) under convex and closed uncertainty sets for the desired signal…
Determining the vanishing points (VPs) in a Manhattan world, as a fundamental task in many 3D vision applications, consists of jointly inferring the line-VP association and locating each VP. Existing methods are, however, either sub-optimal…
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper we explore non-convex boosting in classification by means of integer programming and demonstrate real-world…
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Distributed optimization advances centralized machine learning methods by enabling parallel and decentralized learning processes over a network of computing nodes. This work provides an accelerated consensus-based distributed algorithm for…
We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a…
We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…
The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal…