Related papers: A Riemannian quasi-Newton algorithm for optimizati…
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…
We introduce a proximal limited--memory quasi--Newton scheme for minimizing the sum of a continuously differentiable function and a proper, lower semicontinuous and prox-bounded, possibly nonsmooth, function. Both functions might be…
Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…
We introduce some new proximal quasi-Newton methods for unconstrained multiobjective optimization problems (in short, UMOP), where each objective function is the sum of a twice continuously differentiable strongly convex function and a…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement…
This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…
While first-order methods are popular for solving optimization problems that arise in large-scale deep learning problems, they come with some acute deficiencies. To diminish such shortcomings, there has been recent interest in applying…
This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
Quasi-Newton methods are ubiquitous in deterministic local search due to their efficiency and low computational cost. This class of methods uses the history of gradient evaluations to approximate second-order derivatives. However, only…
Non-asymptotic convergence analysis of quasi-Newton methods has gained attention with a landmark result establishing an explicit local superlinear rate of O$((1/\sqrt{t})^t)$. The methods that obtain this rate, however, exhibit a well-known…
We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and…
Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may…
In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties:…
This work studies the usage of well-known smoothed total variation regularization for solving an atmospheric tomography problem named as {\em GPS-tomography} in some quasi-Newton methods. That is we solve an unconstrained, convex, smooth…