Related papers: Mirror version of similar triangles method for con…
Global optimization finds applications in a wide range of real world problems. The multi-start methods are a popular class of global optimization techniques, which are based on the ideas of conducting local searches at multiple starting…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…
Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…
Network utility maximization is the most important problem in network traffic management. Given the growth of modern communication networks, we consider the utility maximization problem in a network with a large number of connections…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
Shortened abstract: Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates this paper, which…
In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…
In this paper, we describe a stochastic adaptive fast gradient descent method based on the mirror variant of similar triangles method. To our knowledge, this is the first attempt to use adaptivity in stochastic method. Additionally, a main…