Optimization Online


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

Christian Günther (Christian.Guenther***at***mathematik.uni-halle.de)
Christiane Tammer (Christiane.Tammer***at***mathematik.uni-halle.de)

Abstract: 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.

Keywords: multi-objective optimization; Pareto efficiency; constrained optimization; unconstrained optimization; generalized convexity; location theory; gauges

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Mathematical Methods of Operations Research, October 2016, Volume 84, Issue 2, pp 359–387 (DOI: 10.1007/s00186-016-0547-z)


Entry Submitted: 11/04/2015
Entry Accepted: 11/12/2015
Entry Last Modified: 01/23/2018

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society