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Abstract
En 中文
This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous function space to maximize the cost, and the outer problem finds the optimal decision in a Euclidean space to minimize the cost. A solution algorithm is designed to alternately generate the worst-case objective function at the current decision and the optimal decision for the current collection of objective functions. Using operator theory, we prove that this algorithm converges to the defined “semi-global” saddle point of the ObRO problem. In addition, we propose a numerical solver based on the piece-wise linearization (PWL) approximation of objective functions. The PWL approximate problem is proved to be numerically consistent with the original ObRO problem. The obtained results are applied to the degradation-aware battery charging scheduling in distribution networks.
Keywords:
robust optimization
functional uncertainty
minimax optimization
saddle point
operator
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W
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