Related papers: An Inexact First-order Method for Constrained Nonl…
The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly,…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost…
The paper addresses general constrained and non-linear optimization problems. For some of these notoriously hard problems, there exists a reformulation as an unconstrained, global optimization problem. We illustrate the transformation, and…
In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…
This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
This paper presents a numerical function optimization framework designed for constrained optimization problems in robotics. The tool is designed with real-time considerations and is suitable for online trajectory and control input…