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**An all-linear programming relaxation algorithm for optimizing over the efficient set.**
*(English)*
Zbl 0739.90056

Summary: The problem (P) of optimizing a linear function over the efficient set of a multiple objective linear program has many important applications in multiple criteria decision making. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, it appears that no precisely-delineated implementable algorithm exists for solving problem (P) globally. A relaxation algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact optimal solution to the problem after a finite number of iterations. A detailed discussion is included of how to implement the algorithm using only linear programming methods. Convergence of the algorithm is proven, and a sample problem is solved.

### MSC:

90C29 | Multi-objective and goal programming |

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

90B50 | Management decision making, including multiple objectives |

### Keywords:

efficient set of a multiple objective linear program; multiple criteria decision making; relaxation algorithm; globally optimal solution; Convergence
Full Text:
DOI

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