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In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We explain how the discretized two-stage SLCP may be solved by the well-known progressive hedging method (PHM). Moreover, we extend the discussion by considering a two-stage distributionally robust LCP (DRLCP) with moment constraints and proposing a discretization scheme for the DRLCP. As an application, we show how the SLCP and DRLCP models can be used to study equilibrium arising from two-stage duopoly game where each player plans to set up its optimal capacity at present with anticipated competition for production in future.
Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage
In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm, for solvi
Square-root (loss) regularized models have recently become popular in linear regression due to their nice statistical properties. Moreover, some of these models can be interpreted as the distributionally robust optimization counterparts of the tradit
The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. We also explore a number of variants where a
We study safe, data-driven control of (Markov) jump linear systems with unknown transition probabilities, where both the discrete mode and the continuous state are to be inferred from output measurements. To this end, we develop a receding horizon es