我們提出了一系列逆向最佳化模型來預測數學規劃模型的目標係數和線性限制式參數。在線性限制式的最佳化問題下，分別考慮兩種目標函數類型：線性目標式及非線性目標式。所參考的逆向最佳化文獻主要來自Ahuja和Orlin （2001）及Bertsimas等人 （2015）。前者為線性逆向最佳化建立了一般型式的模型，他們試著找到最接近原始參數 c 的 c^，且能使觀察值近似最佳解。後者將此概念用於平衡解，並使用變分不等式(variational inequality)來估計目標函數。 在本論文中，我們根據不同假設建立了五個逆向最佳化模型，並利用自行合成數據(synthetic data)來對模型進行數值驗證，在各個實驗中我們考慮了不同的問題大小及樣本數量。

We propose a series of inverse optimization models to estimate cost coefficients and value of right hand sides for linearly constrained mathematical programming models at different levels of observations. For the types of linearly constrained models to be estimated, we consider two objective function assumptions: linear objective and non-linear objective. The approach we used is related to inverse optimization literature: Ahuja and Orlin (2001) built an inverse optimization model for a linear forward optimization program. They try to find the c^ closet to the given objective parameter c and make the observation approximate to optimal. Bertsimas et al. (2015) enabled the estimation of the objective functions with the observations of the equilibrium based on an inverse variational inequality formulation. In this thesis, five different experiments are done to validate the models using synthetic data.

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