Séminaire FDD-FiME // K. Liu

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Séminaire FDD-FiME // K. Liu

21 octobre 2022 @ 14 h 00 min - 15 h 00 min

Kang Liu (CMAP, Ecole Polytechnique)
Title :  Large-scale nonconvex optimization: randomization, gap estimation, and numerical resolution
Abstract : We address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this problem, obtained by randomization. The relaxation gap is proved to converge to zeros as N goes to infinity, independently of the dimension of the aggregate. We propose a stochastic method to construct an approximate minimizer of the original problem, given an approximate solution of the randomized problem. McDiarmid's concentration inequality is used to quantify the probability of success of the method. We consider the Frank-Wolfe (FW) algorithm for the resolution of the randomized problem. Each iteration of the algorithm requires to solve a subproblem which can be decomposed into N independent optimization problems. A sublinear convergence rate is obtained for the FW algorithm. In order to handle the memory overflow problem possibly caused by the FW algorithm, we propose a stochastic Frank-Wolfe (SFW) algorithm, which ensures the convergence in both expectation and probability senses. Numerical experiments on a mixed-integer quadratic program and an aggregative optimal control problem illustrate the efficiency of the method.
A joint work with J. Frédéric Bonnans, Nadia Oudjane, Laurent Pfeiffer, Cheng Wan


Date :
21 octobre 2022
Heure :
14 h 00 min - 15 h 00 min


Institut Henri Poincaré