Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via Conditional Value at Risk and Difference of Convex Functions

Sun, Hailin; Xu, Huifu; Wang, Yong

doi:10.1007/s10957-012-0127-1

Cited by 30 publications

(12 citation statements)

References 27 publications

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“…are the mean square estimation error of distance and azimuth, respectively. Both of them are related to the signal-to-noise ratio (SNR) of the echo at the current moment and can be calculated as [26]:…”

Section: Observation Modelmentioning

confidence: 99%

Joint Dwell Time and Bandwidth Optimization for Multi-Target Tracking in Radar Network Based on Low Probability of Intercept

Ding

Shi

Qiu

et al. 2020

Sensors

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Radar network systems have been demonstrated to offer numerous advantages for target tracking. In this paper, a low probability of intercept (LPI)-based joint dwell time and bandwidth optimization strategy is proposed for multi-target tracking in a radar network. Since the Bayesian Cramer–Rao lower bound (BCRLB) provides a lower bound on parameter estimation, it can be utilized as the accuracy metric for target tracking. In this strategy, in order to improve the LPI performance of the radar network, the total dwell time consumption of the underlying system is minimized, while guaranteeing a predetermined tracking accuracy. There are two adaptable parameters in the optimization problem: one for dwell time, and the other for bandwidth allocation. Since the nonlinear programming-based genetic algorithm (NPGA) can solve the nonlinear problem well, we develop a method based upon NPGA to solve the resulting problem. The simulation results demonstrate that the proposed strategy has superiority over traditional algorithms, and can achieve a better LPI performance of this radar network.

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Section: Observation Modelmentioning

confidence: 99%

Joint Dwell Time and Bandwidth Optimization for Multi-Target Tracking in Radar Network Based on Low Probability of Intercept

Ding

Shi

Qiu

et al. 2020

Sensors

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“…Remark IV.2. (Existing sample average approximations to CVaR and stochastic VI): The works [27] and [28] study stochastic optimization problems where CVaR is either being minimized or used to define the constraints. Both employ the sample average approximation as proposed in (5) and study asymptotic consistency and exponential convergence of the Karush-Kuhn-Tucker (KKT) points.…”

Section: Sample Average Approximation Of Cwementioning

confidence: 99%

Sample average approximation of CVaR-based Wardrop equilibrium in routing under uncertain costs

Cherukuri

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper focuses on the class of routing games that have uncertain costs. Assuming that agents are riskaverse and select paths with minimum conditional value-atrisk (CVaR) associated to them, we define the notion of CVaRbased Wardrop equilibrium (CWE). We focus on computing this equilibrium under the condition that the distribution of the uncertainty is unknown and a set of independent and identically distributed samples is available. To this end, we define the sample average approximation scheme where CWE is estimated with solutions of a variational inequality problem involving sample average approximations of the CVaR. We establish two properties for this scheme. First, under continuity of costs and boundedness of uncertainty, we prove asymptotic consistency, establishing almost sure convergence of approximate equilibria to CWE as the sample size grows. Second, under the additional assumption of Lipschitz cost, we prove exponential convergence where the probability of the distance between an approximate solution and the CWE being smaller than any constant approaches unity exponentially fast. Simulation example validates our theoretical findings.

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“…In fact, when C(u) and (u, y) are convex with respect to variable u, problems (P1) and (P2) are equivalent in the sense that they have the same optimal value (see previous studies 28,31 ). The proposition below gives some sufficient conditions for the convexity of (u, p) with respect to u.…”

Section: Remarkmentioning

confidence: 99%

“…Both objective and constraints are involved random variables in our RRLD model; The other is the approximation of chance constraints for security limits. A CVaR approximation is adopted, which has some advantages in mathematics . Furthermore, we establish some theoretical analysis for modeling reformulation.…”

Section: Introductionmentioning

confidence: 99%

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A distributionally robust optimization-based risk-limiting dispatch in power system under moment uncertainty

Tong¹,

Luo

Yang

et al. 2017

Int. Trans. Electr. Energ. Syst.

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Summary In this paper, we study the risk‐limiting dispatch (RLD) of power system in the case that the distribution information of random variable is ambiguous. Under an ellipsoidal moment uncertainty of the mean and the covariance matrix, we develop the distributionally robust optimization approach to set up a new RLD model, named robust RLD (RRLD for short). The RRLD considers simultaneously the risk of unsafe operation limit by conditional Value‐at‐Risk management. We further convert the RRLD model into a solvable convex optimization for a special case that the operation constraint is addressed on the overloading transmission current. The new RRLD model is a development and generalization of the traditionary economic dispatch and the RLD approach. Meanwhile, our research extends the distributionally robust optimization application in portfolio problems to a security economic operation of power system. The IEEE‐14 and IEEE‐30 bus system are chosen as numerical test systems. Preliminary numerical examples show the validity of the model and its reformulation.

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Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via Conditional Value at Risk and Difference of Convex Functions

Cited by 30 publications

References 27 publications

Joint Dwell Time and Bandwidth Optimization for Multi-Target Tracking in Radar Network Based on Low Probability of Intercept

Joint Dwell Time and Bandwidth Optimization for Multi-Target Tracking in Radar Network Based on Low Probability of Intercept

Sample average approximation of CVaR-based Wardrop equilibrium in routing under uncertain costs

A distributionally robust optimization-based risk-limiting dispatch in power system under moment uncertainty

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