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Nonlinear Multiobjective Programming

  1. Alexander Engau

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0810

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Engau, A. 2011. Nonlinear Multiobjective Programming. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Colorado Denver, Department of Mathematical and Statistical Sciences, Denver, Colorado

Publication History

  1. Published Online: 15 FEB 2011

Abstract

This introductory treatment of the theory and methodology of nonlinear multiobjective programming offers an annotated bibliographic overview of various concepts and approaches to solve continuous deterministic multicriteria optimization problems. First, the notions of Pareto optimality, efficiency, and nondominance are discussed and then related to approximate, epsilon, and proper efficiency. Second, after highlighting similarities and pointing out differences to first- and second-order optimality conditions in classical nonlinear programming, several other topics including duality and sensitivity are also mentioned. Third, a number of solution approaches and generating methods are described with a particular focus on scalarizations using objective aggregation, prioritization, and norm or distance minimization to some utopian reference point.

Keywords:

  • annotated survey;
  • nonlinear multiobjective programming;
  • multicriteria optimization;
  • vector optimization;
  • partial orders;
  • ordering cones;
  • Pareto optimality;
  • efficiency;
  • approximate efficiency;
  • epsilon efficiency;
  • proper efficiency;
  • trade-offs;
  • efficient solutions;
  • nondominance;
  • nondominated points;
  • optimality conditions;
  • duality;
  • sensitivity;
  • scalarization;
  • generating methods;
  • weighted sum;
  • epsilon-constraint;
  • Chebyshev norm