The two-stage stochastic variational inequality (SVI) provides a powerful modeling paradigm for many important applications in which uncertainties and equilibrium are present. This talk reviews some new theory and algorithms for the two-stage SVI. Moreover, we formulate a convex two-stage non-cooperative multi-agent game under uncertainty as a two-stage SVI. Numerical results based on historical data in crude oil market are presented to demonstrate the effectiveness of the two-stage SVI in describing the market share of oil producing agents.
Linear programming (LP) is fundamentally important in mathematical optimization. In this talk, we review the following two methods: the LP-Newton method for LPs with box constraints proposed by Fujishige et al. , LPS-Newton method proposed by Kitahara et al. Inspired by the methods we develop a new method that uses facets information of the constraints for solving PLs with box constraints because an optimal solution can be found at an intersection between a zonotope and a line. We also report several results of preliminary experiments showing the efficiency of the proposed algorithm.
In this paper, we attempt to provide a decision-practical foundation for optimal rebalancing strategies of an existing financial portfolio. our main concern is the development of a sparse and diversified portfolio rebalancing model in the worst-case CVaR framework, considering transaction costs and double cardinality constraints that trade off between the limits of investment scale and industry coverage requirements simultaneously. We propose an efficient ADMM to conduct out-of-sample performance analysis of our proposed strategy on actual data from the Chinese stock market.