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Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…
This paper analyzes the contraction of the primal-dual gradient optimization via contraction theory in the context of discrete-time updating dynamics. The contraction theory based on Riemannian manifolds is first established for convergence…
In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…
The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel…
Spectral compressed sensing involves reconstructing a spectral-sparse signal from a subset of uniformly spaced samples, with applications in radar imaging and wireless channel estimation. By fully exploiting the signal structures, this…
Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We propose a novel evolutionary algorithm for optimizing real-valued objective functions defined on the Grassmann manifold Gr}(k,n), the space of all k-dimensional linear subspaces of R^n. While existing optimization techniques on Gr}(k,n)…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$…
Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…
Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…