On the inverse problem of linear programming and its application to minimum weight perfect k-matching

Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to find a minimal adjustment of the cost function such that the given solution becomes optimum.Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods for solving them. Then we discuss the problems considered in the literature and the results that have been obtained. Finally, we formulate some open problems.

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“…They formulate the inverse linear programming problem as a new linear program. Huang and Liu [23] achieve the same result.…”

Section: The Inverse Linear Programming Problemmentioning

confidence: 55%

“…Using their linear programming results, Huang and Liu [23] prove that the unconstrained single object case under unit weight l 1 norm can be transformed to a minimum cost circulation problem in a bipartite graph. Note that Theorem 3.1 implies that the inverse problem equals the original problem.…”

Section: Minimum Weight Bipartite Perfect K-matchingmentioning

confidence: 99%

Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results

Heuberger

2004

Journal of Combinatorial Optimization

275

152

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“…On the other hand in the field of operational research many applications have been reported using inverse linear programming problem that first was introduced by Zhang and Liu (1996) and further improved by Huang and Liu (1999). The first application of inverse linear programming was the shortest paths problems as developed by Toint (1992a, 1992b).…”

Section: Introductionmentioning

confidence: 99%

“…Other applications include the shortest arborescence problem (Hu & Liu, 1998), maximum capacity problems (Yang & Zhang, 1998) and the maximum flow and minimum cut problems (Burkard, Klinz, & Zhang, 2001;Yang, Zhang, & Ma, 1997). Many more applications of inverse linear programming have been reported by Huang and Liu (1999).…”

Section: Introductionmentioning

confidence: 99%

Inverse forecasting: A new approach for predictive modeling

Amin

Emrouznejad

2007

Computers & Industrial Engineering

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“…The research on inverse optimization problems have attracted some attention over the last decade. For example, Burton and Toint [3], [4] and Burton, Pulleyblank and Toint [5], Ahuja and Orlin [1], Dial [6] have studied inverse shortest path problem, Huang and Liu [7], [8] have considered inverse linear programming and applied it to inverse matching problem and inverse minimum cost flow problem respectively; Zhang, Liu and Ma [12], Sokkalingam, Ahuja and Orlin [1], and Ahuja and Orlin [2] studied inverse minimum spanning tree problem. For a survey on inverse combinatorial optimization problems we refer the reader to Ahuja and Orlin [1], and Hueberger [9].…”

Section: Introductionmentioning

confidence: 99%