5 citations · 11 across the 21 of their papers we have counts for
24 papers
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…
Randomized subspace gradient method for constrained optimization
Ryota Nozawa, Pierre-Louis Poirion, Akiko Takeda
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization proble…
The Maximum Matrix Contraction Problem
Dimitri Watel, Pierre-Louis Poirion
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the comp…
Theoretical analysis of the randomized subspace regularized Newton method for non-convex optimization
Terunari Fuji, Pierre-Louis Poirion, Akiko Takeda
While there already exist randomized subspace Newton methods that restrict the search direction to a random subspace for a convex function, we propose a randomized subspace regular…
Convexification with bounded gap for randomly projected quadratic optimization
Terunari Fuji, Pierre-Louis Poirion, Akiko Takeda
Random projection techniques based on Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preser…
Random projections for conic programs
Leo Liberti, Pierre-Louis Poirion, Ky Vu
We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility…
Random projection of Linear and Semidefinite problem with linear inequalities
Pierre-Louis Poirion, Bruno F. Lourenço, Akiko Takeda
The Johnson-Lindenstrauss Lemma states that there exist linear maps that project a set of points of a vector space into a space of much lower dimension such that the Euclidean dist…
Formulations for designing robust networks. An application to wind power collection
Cédric Bentz, Marie-Christine Costa, Pierre-Louis Poirion +1
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminal…
Robust capacitated trees and networks with uniform demands
Cédric Bentz, Marie-Christine Costa, Pierre-Louis Poirion +1
We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and…
Adaptive Network Flow with -Arc Destruction
Thomas Ridremont, Dimitri Watel, Pierre-Louis Poirion +1
When a flow is not allowed to be reoriented the Maximum Residual Flow Problem with -Arc Destruction is known to be -hard for . We show that when a flow is allowed to be…
Random projections for linear programming
Ky Vu, Pierre-Louis Poirion, Leo Liberti
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves a…
Random projections for trust region subproblems
Ky Vu, Pierre-Louis Poirion, Claudia D'Ambrosio +1
The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear…
On an optimal constraint aggregation method for integer programming and on an analytic expression of the number of integer points in a polytope
Pierre-Louis Poirion, Vu Khac Ky, Leo Liberti
In this paper we give a new aggregation framework for linear Diophantine equations. In particular, we prove that an aggregated system of minimum size can be built in polynomial tim…
Gaussian random projections for Euclidean membership problems
Ky Vu, Pierre-Louis Poirion, Leo Liberti
We discuss the application of random projections to the fundamental problem of deciding whether a given point in a Euclidean space belongs to a given set. We show that, under a num…
Using the Johnson-Lindenstrauss lemma in linear and integer programming
Ky Vu, Pierre-Louis Poirion, Leo Liberti
The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such a…