Mathematical Methods of Operations Research

, Volume 84, Issue 2, pp 359–387 | Cite as

Relationships between constrained and unconstrained multi-objective optimization and application in location theory

  • Christian Günther
  • Christiane Tammer


This article deals with constrained multi-objective optimization problems. The main purpose of the article is to investigate relationships between constrained and unconstrained multi-objective optimization problems. Under suitable assumptions (e.g., generalized convexity assumptions) we derive a characterization of the set of (strictly, weakly) efficient solutions of a constrained multi-objective optimization problem using characterizations of the sets of (strictly, weakly) efficient solutions of unconstrained multi-objective optimization problems. We demonstrate the usefulness of the results by applying it on constrained multi-objective location problems. Using our new results we show that special classes of constrained multi-objective location problems (e.g., point-objective location problems, Weber location problems, center location problems) can be completely solved with the help of algorithms for the unconstrained case.


Multi-objective optimization Pareto efficiency Constrained optimization Unconstrained optimization Generalized convexity Location theory Gauges 



The authors wish to thank the anonymous referees for their valuable comments.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of Natural Sciences II, Institute for MathematicsMartin Luther University Halle-WittenbergHalle (Saale)Germany

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