A class of two-stage distributionally robust games

Li, Bin; Sun, Jie; Xu, Honglei; Zhang, Min

doi:10.3934/jimo.2018048

Cited by 19 publications

(17 citation statements)

References 41 publications

(61 reference statements)

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“…The case when k > 1 can be used to combine different risk measures, for instance, if k = 2, we can define ρ(Z) = E(Z) + [E|Z − τ | p ] 1/p , where p ≥ 2. In order to solve (4) with ρ having the form like (19), the first problem is to solve the subproblem (10). We have the next result.…”

Section: Proof Denotementioning

confidence: 99%

“…Suppose that P is a probability measure on a measurable space (Ω, F), and that every finite subset of Ω is F-measurable. Let s = k+p+q+1, where k, p, q are defined in (19), (16) and Theorem 2.2 respectively. If the risk measure ρ P has the form of (19), then for any x ∈ X, the inner maximum problem (10) is equivalent to the following problem…”

Section: Proof Denotementioning

confidence: 99%

“…In Sun et al [31], the objective function is the sum of a quadratic cost of the first stage and a risk measure of the quadratic recourse cost of the second stage. Other related study on distributionally robust optimization and control can be found in [19,17,18]. In current literatures on distributionally robust optimization, most study focus on the case that the objective functions are expected value functions.…”

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confidence: 99%

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Robust stochastic optimization with convex risk measures: A discretized subgradient scheme

Yu¹,

Sun²

2021

Journal of Industrial &Amp; Management Optimization

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We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method.2010 Mathematics Subject Classification. Primary: 90C15; 90C47.

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Section: Proof Denotementioning

confidence: 99%

Section: Proof Denotementioning

confidence: 99%

mentioning

confidence: 99%

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Robust stochastic optimization with convex risk measures: A discretized subgradient scheme

Yu¹,

Sun²

2021

Journal of Industrial &Amp; Management Optimization

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“…Remark 3: For the inequality constraints (16) of Theorem 1 and (31) of Theorem 2, the Matlab LMI toolbox can be used to obtain the results. For the equation constraint conditions of Equations (15) and (30), they can be transformed into the corresponding LMI conditions [25]- [27] as follows:…”

Section: Remarkmentioning

confidence: 99%

Design of LPV fault-tolerant controller for hypersonic vehicle based on state observer

Cai¹,

Zhao²,

Quan³

et al. 2021

Journal of Industrial &Amp; Management Optimization

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Considering the parameter uncertainty and actuator failure of hypersonic vehicle during maneuvering, this paper proposes a state observerbased hypersonic vehicle fault-tolerant control (FTC) system design method. Because hypersonic vehicles are prone to failure during maneuvering, the state quantity cannot be measured. First, a state observer-based FTC control method is designed for the linear parameter-varying (LPV) model with parameter uncertainty and partial failure of the actuator. Then, the Lyapunov function is used to demonstrate the asymptotic stability of the closed-loop system. The performance index function proved that the system has robust stability under the disturbance condition. Subsequently, the linear matrix inequality (LMI) was used to solve the observer parameters and the corresponding gain matrix in the control system. The simulation results indicated that the designed controller can track the flight command signal stably and has strong robustness, which verified the effectiveness of the design controller.

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“…[24] converted the risk-averse two-stage stochastic programming model into a semidefinite programming problem. [22] and [23] considered consider distributionally robust two-stage stochastic convex programming problems with ambiguity sets proposed by [50], and converted this class of problems to a conic optimization problems. [26] proposed a data-driven two-stage distributionally optimization framework with φ− divergences constrained and presented a decomposition-based solution algorithm to solve the resulting models.…”

mentioning

confidence: 99%

Multi-stage distributionally robust optimization with risk aversion

Huang¹,

Qu²,

Yang³

et al. 2021

Journal of Industrial &Amp; Management Optimization

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Two-stage risk-neutral stochastic optimization problem has been widely studied recently. The goals of our research are to construct a two-stage distributionally robust optimization model with risk aversion and to extend it to multi-stage case. We use a coherent risk measure, Conditional Value-at-Risk, to describe risk. Due to the computational complexity of the nonlinear objective function of the proposed model, two decomposition methods based on cutting planes algorithm are proposed to solve the two-stage and multi-stage distributional robust optimization problems, respectively. To verify the validity of the two models, we give two applications on multi-product assembly problem and portfolio selection problem, respectively. Compared with the risk-neutral stochastic optimization models, the proposed models are more robust.

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A class of two-stage distributionally robust games

Cited by 19 publications

References 41 publications

Robust stochastic optimization with convex risk measures: A discretized subgradient scheme

Robust stochastic optimization with convex risk measures: A discretized subgradient scheme

Design of LPV fault-tolerant controller for hypersonic vehicle based on state observer

Multi-stage distributionally robust optimization with risk aversion

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