Abstract
For obtaining the set of all quasi-supremal index vectors (or all maximal index vectors, or all Pareto-optimal solutions) of a multiple-objective optimization problem, we present, in this paper, the method of proper inequality constraints, which does not rely on any convexity condition at all, but by which one can obtain the entire desired set. This method is based on the observation that optimizing the index of one of the objectives, with some arbitrary bounds assigned to all other objectives, may still result in inferior solutions, unless these bounds areproper. Various necessary and/or sufficient conditions are presented for the properness test.
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Lin, J. G.,Maximal Vectors and Multi-Objective Optimization, Journal of Optimization Theory and Applications, Vol. 18, No. 1, 1976.
Lin, J. G.,Proper Equality Constraints and Maximization of Index Vectors, Journal of Optimization Theory and Applications, Vol. 20, No. 4, 1976.
Lin, J. G.,Circuit Design under Multiple Performance Objectives, Proceedings of 1974 IEEE International Symposium on Circuits and Systems, San Francisco, California, 1974.
Lin, J. G.,Three Methods for Determining Pareto-Optimal Solutions of Multiple-Objective Optimization Problems, Directions in Large-Scale Systems: Decentralized Control and Many-Person Optimization, Edited by Y. C. Ho and S. K. Mitter, Plenum Press, New York, New York, 1976.
Lin, J. G.,Multiple-Objective Optimization, Columbia University, Department of Electrical Engineering and Computer Science, Systems Research Group, Technical Report, 1972.
Lin, J. G.,Multiple-Objective Problems: Pareto-Optimal Solutions by Method of Proper Equality Constraints, IEEE Transactions on Automatic Control, Vol. AC-21, No. 5, 1976.
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Communicated by P. Varaiya
This work was supported by the National Science Foundation under Grant No. GK-32701.
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Lin, J.G. Proper inequality constraints and maximization of index vectors. J Optim Theory Appl 21, 505–521 (1977). https://doi.org/10.1007/BF00933094
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DOI: https://doi.org/10.1007/BF00933094