Related papers: Manopt, a Matlab toolbox for optimization on manif…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

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,…

Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…

Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

The problem of optimization on Stiefel manifold, i.e., minimizing functions of (not necessarily square) matrices that satisfy orthogonality constraints, has been extensively studied. Yet, a new approach is proposed based on, for the first…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, we explore the application of those strategies to Riemannian optimization, wherein minimization is to be…

The optimization and machine learning toolkit (OMLT) is an open-source software package incorporating neural network and gradient-boosted tree surrogate models, which have been trained using machine learning, into larger optimization…

Convex optimization is an essential tool for machine learning, as many of its problems can be formulated as minimization problems of specific objective functions. While there is a large variety of algorithms available to solve convex…

This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence…

The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical…

NonOpt, a C++ software package for minimizing locally Lipschitz objective functions, is presented. The software is intended primarily for minimizing objective functions that are nonconvex and/or nonsmooth. The package has implementations of…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…

Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a…

Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…