10 papers · 1 filter
Random-Subspace Frank--Wolfe over Strongly Convex Sets
Pierre-Louis Poirion, Sebastian Pokutta, Akiko Takeda
Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduc…
Randomized Subspace Nesterov Accelerated Gradient
Gaku Omiya, Pierre-Louis Poirion, Akiko Takeda
Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode a…
Fairness in Robust Unit Commitment Problem Considering Suppression of Renewable Energy
Ichiro Toyoshima, Pierre-Louis Poirion, Tomohide Yamazaki +4
Power company operators make power generation plans one day in advance, in what is known as the Unit Commitment (UC) problem. UC is exposed to uncertainties, such as unknown electr…
Convergence Analysis of Randomized Subspace Normalized SGD under Heavy-Tailed Noise
Gaku Omiya, Pierre-Louis Poirion, Akiko Takeda
Randomized subspace methods reduce per-iteration cost; however, in nonconvex optimization, most analyses are expectation-based, and high-probability bounds remain scarce even under…
Inexact subgradient algorithm with a non-asymptotic convergence guarantee for copositive programming problems
Mitsuhiro Nishijima, Pierre-Louis Poirion, Akiko Takeda
In this paper, we propose a subgradient algorithm with a non-asymptotic convergence guarantee to solve copositive programming problems. The subproblem to be solved at each iteratio…
Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method
Andi Han, Pierre-Louis Poirion, Akiko Takeda
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these prob…
Sparse Sub-gaussian Random Projections for Semidefinite Programming Relaxations
Monse Guedes-Ayala, Pierre-Louis Poirion, Lars Schewe +1
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of…
Subspace Quasi-Newton Method with Gradient Approximation
Taisei Miyaishi, Ryota Nozawa, Pierre-Louis Poirion +1
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to…
Improving Convergence Guarantees of Random Subspace Second-order Algorithm for Nonconvex Optimization
Rei Higuchi, Pierre-Louis Poirion, Akiko Takeda
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as i…
Zeroth-order Random Subspace Algorithm for Non-smooth Convex Optimization
Ryota Nozawa, Pierre-Louis Poirion, Akiko Takeda
Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Altho…