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Cone Characterizations of Approximate Solutions in Real Vector Optimization

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Abstract

Approximate nondominated solutions of real vector optimization problems are characterized using the concept of translated cones. Relationships between these solutions and Pareto nondominated points are examined, and the problem of optimizing over the set of approximate solutions is addressed.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, USA

    A. Engau & M. M. Wiecek

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  1. A. Engau
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  2. M. M. Wiecek
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Correspondence to A. Engau.

Additional information

Communicated by H.P. Benson

This research was supported by the National Science Foundation, Grant DMS-0425768, and by the Automotive Research Center, a US Army TACOM Center of Excellence for Modeling and Simulation of Ground Vehicles at the University of Michigan

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Engau, A., Wiecek, M.M. Cone Characterizations of Approximate Solutions in Real Vector Optimization. J Optim Theory Appl 134, 499–513 (2007). https://doi.org/10.1007/s10957-007-9235-8

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