## A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set.(English)Zbl 0794.90048

Summary: The problem (P) of optimizing a linear function over the efficient set of a multiple-objective linear program serves many useful purposes in multiple-criteria decision making. Mathematically, problem (P) can be classified as a global optimization problem. Such problems are much more difficult to solve than convex programming problems. In this paper, a nonadjacent extreme-point search algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact extreme-point optimal solution for the problem after a finite number of iterations. It can be implemented using only linear programming methods. Convergence of the algorithm is proven, and a discussion is included of its main advantages and disadvantages.

### MSC:

 90C29 Multi-objective and goal programming 90C26 Nonconvex programming, global optimization 90C05 Linear programming
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### References:

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