The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for wh...
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The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for which scenario a prescribed optimal value is attained. Using continuity of the optimal value function (under some assumptions), we propose a method based on parametric linearprogramming techniques. We study special cases when the interval coefficients are situated in the objective function and/or on the right-hand sides of the constraints as well as the generic case when possibly all coefficients are intervals. We also compare our method with the straightforward binary search technique. Finally, we illustrate the theory by an accompanying numerical study, called "Matrix Casino", showing some approaches to designing a matrix game with a prescribed game value. (C) 2015 Elsevier B.V. All rights reserved.
inverse linear programming (LP) has received increasing attention because of its potential to infer efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely i...
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inverse linear programming (LP) has received increasing attention because of its potential to infer efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and corresponding forward solutions from the existing inverse LP methods can be highly sensitive to noise, errors, and uncertainty in the input data, limiting their applicability in data-driven settings. We introduce the notion of inverse and forward stability in inverse LP and propose a novel inverse LP method that determines a set of objective functions that are stable under data imperfection and generate forward solutions close to the relevant subset of the data. We formulate the inverse model as a large-scale mixed-integer program (MIP) and elucidate its connection to biclique problems, which we exploit to develop efficient algorithms that solve much smaller MlPs instead to construct a solution to the original problem. We numerically evaluate the stability of the proposed method and demonstrate its use in the diet recommendation and transshipment applications.
In the last two decades there have been substantial developments in the mathematical theory of inverse optimization problems, and their applications have expanded greatly. In parallel, time series analysis and forecas...
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In the last two decades there have been substantial developments in the mathematical theory of inverse optimization problems, and their applications have expanded greatly. In parallel, time series analysis and forecasting have become increasingly important in various fields of research such as data mining, economics, business, engineering, medicine, politics, and many others. Despite the large uses of linearprogramming in forecasting models there is no a single application of inverse optimization reported in the forecasting literature when the time series data is available. Thus the goal of this paper is to introduce inverse optimization into forecasting field, and to provide a streamlined approach to time series analysis and forecasting using inverse linear programming. An application has been used to demonstrate the use of inverse forecasting developed in this study. (c) 2007 Elsevier Ltd. All rights reserved.
We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decisi...
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We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decision-maker who (approximately) solves an optimization problem and cluster the data points by identifying a common objective function of the optimization problems for each cluster such that the worst-case optimality error is minimized. We propose three different clustering models and test them in the diet recommendation application. (C) 2021 Elsevier B.V. All rights reserved.
inverse linear programming problem (ILPb) by modifying the right-hand vector is discussed in the paper. A mathematical model of (ILPb), which is an MPEC problem, is constructed based on duality theories, and then ...
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inverse linear programming problem (ILPb) by modifying the right-hand vector is discussed in the paper. A mathematical model of (ILPb), which is an MPEC problem, is constructed based on duality theories, and then a necessary and sufficient condition of checking the feasibility of (ILPb) is provided. The inverse problem under (1 norm is transformed into a problem under weighted sum-type Hamming distance with linear equality and inequality constraints. An optimal solution in the special case is also given when the dual constraint conditions are all equalities and the coefficient matrix is invertible. In this case, the system of linear equations has the only solution.
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