[00223] Stochastic optimization and stochastic variational inequalities
Session Time & Room : 3D (Aug.23, 15:30-17:10) @A201
Type : Proposal of Minisymposium
Abstract : Stochastic optimization and stochastic variational inequalities are important mathematical tools for decision-making problems and equilibrium problems under uncertainty. This mini-symposium brings several researchers in stochastic optimization and stochastic variational inequalities together and offers an opportunity to discuss the latest developments.
[02880] Dynamic Stochastic Projection Method for Multistage Stochastic Variational Inequalities
Format : Talk at Waseda University
Author(s) :
Hailin Sun (Nanjing Normal University)
Bin Zhou (Nanjing Normal University)
Jie Jiang (Chongqing University)
Abstract : Stochastic approximation (SA) type methods have been well studied for solving single-stage stochastic variational inequalities (SVIs). This paper proposes a dynamic stochastic projection method (DSPM) for solving multistage SVIs. In particular, we investigate an inexact single-stage SVI and present an inexact stochastic projection method (ISPM) for solving it. Then we give the DSPM to a three-stage SVI by applying the ISPM to each stage. We show that the DSPM can achieve an $\mathcal{O}(\frac{1}{\epsilon^2})$ convergence rate regarding the total number of required scenarios for the three-stage SVI. We also extend the DSPM to the multistage SVI when the number of stages is larger than three. The numerical experiments illustrate the effectiveness and efficiency of the DSPM.
[02891] A two-stage stochastic variational inequality model
Format : Talk at Waseda University
Author(s) :
Min Li (Beijing Jiaotong University)
Chao Zhang (Beijing Jiaotong University)
Mingxv Ding (Beijing Jiaotong University)
Ruipu Lv (Beijing Jiaotong University)
Abstract : This paper first proposes a new nonsmooth two-stage stochastic equilibrium model of medical supplies in epidemic management. The first stage addresses the storage in the pre-disaster phase, and the second stage focuses on the dynamic distribution in the post-disaster phase. The uncertainties are the numbers of infected people treated in multiple hospitals. The model is further approximated and transformed to a monotone two-stage stochastic variational inequality (SVI) model that is computationally tractable.
[02899] Discrete approximation for two-stage stochastic variational inequalities
Format : Talk at Waseda University
Author(s) :
Jie Jiang (Chongqing University)
Hailin Sun (Nanjing Normal University)
Abstract : In this paper, the discrete approximation of two-stage stochastic variational inequalities has been investigated when the second stage problem has multiple solutions. First, a discrete approximation scheme is given by a series of models with the aid of merit functions. After that, the convergence relationships between these models are analysed, which therefore yields the convergence guarantee of the proposed discrete approximation scheme. Finally, we use the well-known progressive hedging algorithm to report some numerical results and to validate the effectiveness of the discrete approximation approach.
[05136] Iteratively sampling scheme for stochastic optimization with variable number sample path
Format : Online Talk on Zoom
Author(s) :
Dali ZHANG (Shanghai Jiao Tong University)
Shuang HAO (Shanghai Jiao Tong University)
Ming Dong (Shanghai Jiao Tong University)
Abstract : Optimal search methods are proposed for solving optimization problems with analytically unobtainable objectives. This paper proposes a method by incorporating sampling schemes into the directional direct search with variable number sample path and investigates its effectiveness in solving stochastic optimization problems. We also explore the conditions on sample sizes at each iteration under which the convergence in probability can be guaranteed. Finally, a set of benchmark problems are numerically tested to show the effectiveness in different sampling schemes.
