Proof of Soland's conjecture on the efficient solutions to a multicriteria optimization problem

Anas Mifrani

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arXiv · 2502.05180

Proof of Soland's conjecture on the efficient solutions to a multicriteria optimization problem

Anas Mifrani

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Abstract

This note proves Richard M. Soland's conjecture that given an efficient solution to a multicriteria optimization problem, there need not exist a continuous, strictly increasing and strictly concave criterion space function that attains its maximum at the vector of criteria values achieved by that solution. We work out an important implication of this result for multicriteria decision making.

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Anas Mifrani. 2025-01-11. Proof of Soland's conjecture on the efficient solutions to a multicriteria optimization problem. https://arxiv.org/abs/2502.05180

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