Nonlinear Multiobjective Programming

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.

Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization

“…The comparison of these definitions in the sense of Geoffrion [20,26,66] to several other notions of proper efficiency including those by Benson [5], Borwein [9], Borwein and Zhuang [10], Hartley [28] and Henig [30] is discussed in these former papers and several other review articles or monographs [27,37,39,59] that are also included in the author's previous bibliographic survey [18]. In addition, the interesting relationships between existence and density results for proper efficiency based on the Arrow-Barankin-Blackwell theorem [2] and related more recent results [14] has also already been analyzed in some detail by Truong [65].…”