Related papers: On Riemannian Approach for Constrained Optimizatio…

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,…

Many modern multiclass and multilabel problems are characterized by increasingly large output spaces. For these problems, label embeddings have been shown to be a useful primitive that can improve computational and statistical efficiency.…

We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank…

The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and…

In this paper a high speed neural network classifier based on extreme learning machines for multi-label classification problem is proposed and dis-cussed. Multi-label classification is a superset of traditional binary and multi-class…

Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing…

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…

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…

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$. We propose a class of constraint dissolving approaches for these Riemannian optimization…

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…

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily…

Extreme multi-label learning (XML) or classification has been a practical and important problem since the boom of big data. The main challenge lies in the exponential label space which involves $2^L$ possible label sets especially when the…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

The multilabel learning problem with large number of labels, features, and data-points has generated a tremendous interest recently. A recurring theme of these problems is that only a few labels are active in any given datapoint as compared…

For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing…

We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…

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…

A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…