A Generalization of the Monotone Convergence Theorem

Bas, Antonio Linero; Nieves-Roldán, Daniel

doi:10.1007/s00009-021-01785-7

Cited by 3 publications

(2 citation statements)

References 2 publications

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“…g(α) is less than 0, and hence q(α) is a monotone decreasing function. And the inf α {•} of Equation ( 13) can be replaced by lim α→∞ {•}, according to the monotone converge theorem [34]. As α is getting larger, the term of λP tends to be negligible and the optimal P of inner maximization problem tends to be P * ( λ), which recovers Equation (12).…”

Section: Tractable Transformation Of Regretmentioning

confidence: 99%

Electricity Price Prediction for Energy Storage System Arbitrage: A Decision-Focused Approach

Sang

Long

et al. 2022

IEEE Trans. Smart Grid

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Electricity price prediction plays a vital role in energy storage system (ESS) management. Current prediction models focus on reducing prediction errors but overlook their impact on downstream decision-making. So this paper proposes a decision-focused electricity price prediction approach for ESS arbitrage to bridge the gap from the downstream optimization model to the prediction model. The decision-focused approach aims at utilizing the downstream arbitrage model for training prediction models. It measures the difference between actual decisions under the predicted price and oracle decisions under the true price, i.e., decision error, by regret, transforms it into the tractable surrogate regret, and then derives the gradients to predicted price for training prediction models. Based on the prediction and decision errors, this paper proposes the hybrid loss and corresponding stochastic gradient descent learning method to learn prediction models for prediction and decision accuracy. The case study verifies that the proposed approach can efficiently bring more economic benefits and reduce decision errors by flattening the time distribution of prediction errors, compared to prediction models for only minimizing prediction errors.

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Section: Tractable Transformation Of Regretmentioning

confidence: 99%

Electricity Price Prediction for Energy Storage System Arbitrage: A Decision-Focused Approach

Sang

Long

et al. 2022

IEEE Trans. Smart Grid

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show abstract

“…Recently, following this idea, in [23] the classical Monotone Convergence Theorem has been generalized by changing the monotonicity with a convexity condition on the involved functions.…”

Section: Introductionmentioning

confidence: 99%

Convergence Theorems for Varying Measures Under Convexity Conditions and Applications

Marraffa

Satco

2022

Mediterr. J. Math.

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In this paper, convergence theorems involving convex inequalities of Copson’s type (less restrictive than monotonicity assumptions) are given for varying measures, when imposing convexity conditions on the integrable functions or on the measures. Consequently, a continuous dependence result for a wide class of differential equations with many interesting applications, namely measure differential equations (including Stieltjes differential equations, generalized differential problems, impulsive differential equations with finitely or countably many impulses and also dynamic equations on time scales) is provided.

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Three-Dimensional Cooperative Positioning for Internet of Things Provenance

Cui²,

Ni³

et al. 2022

IEEE Internet Things J.

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A Generalization of the Monotone Convergence Theorem

Cited by 3 publications

References 2 publications

Electricity Price Prediction for Energy Storage System Arbitrage: A Decision-Focused Approach

Electricity Price Prediction for Energy Storage System Arbitrage: A Decision-Focused Approach

Convergence Theorems for Varying Measures Under Convexity Conditions and Applications

Three-Dimensional Cooperative Positioning for Internet of Things Provenance

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