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This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While successive pseudospectral convexification combines spectral collocation with successive convexification,…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages. Our approach formulates the alignment learning problem as a domain adaptation problem…
We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are ubiquitous in engineering applications but still largely…
This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel…
Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear…
The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimization problem on the Stiefel manifold that can be solved using…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…
In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This extension is threefold. First, we introduce…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean…
We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…
Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
Landing methods have recently emerged in Riemannian matrix optimization as efficient schemes for handling nonlinear equality constraints without resorting to costly retractions. These methods decompose the search direction into tangent and…
Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property…
Motivated by energy based analyses for descent methods in the Euclidean setting, we investigate a generalisation of such analyses for descent methods over Riemannian manifolds. In doing so, we find that it is possible to derive…