Related papers: A General System for Heuristic Solution of Convex …
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex problem of finding the distance between the boundaries of…
We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a…
SnapVX is a high-performance Python solver for convex optimization problems defined on networks. For these problems, it provides a fast and scalable solution with guaranteed global convergence. SnapVX combines the capabilities of two open…
This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…
Non-convex constrained optimizations are ubiquitous in robotic applications such as multi-agent navigation, UAV trajectory optimization, and soft robot simulation. For this problem class, conventional optimizers suffer from small step sizes…
Optimizing nonconvex (NCVX) problems, especially nonsmooth and constrained ones, is an essential part of machine learning. However, it can be hard to reliably solve such problems without optimization expertise. Existing general-purpose NCVX…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
Optimization aims at selecting a feasible set of parameters in an attempt to solve a particular problem, being applied in a wide range of applications, such as operations research, machine learning fine-tuning, and control engineering,…
MOCVXPY is an open-source Python library for convex vector optimization. It is built on top of CVXPY, a domain-specific language for single-objective convex optimization. MOCVXPY enables practitioners to describe their convex vector…
We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…