Abstract
Recently, sufficient optimality theorems for (weak) Pareto-optimal solutions of a multiobjective optimization problem (MOP) were stated in Theorems 3.1 and 3.3 of Ref. 1. In this note, we give a counterexample showing that the theorems of Ref. 1 are not true. Then, by modifying the assumptions of these theorems, we establish two new sufficient optimality theorems for (weak) Pareto-optimal solutions of (MOP); moreover, we give generalized sufficient optimality theorems for (MOP).
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References
Majumdar, A. A. K., Optimality Conditions in Differentiable Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 92, No. 2, pp. 419–427, 1997.
Singh, C., Optimality Conditions in Multiobjective Differentiable Programming, Journal of Optimization Theory and Applications, Vol. 53, No. 1, pp. 115–123, 1987.
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Kim, D.S., Lee, G.M., Lee, B.S. et al. Counterexample and Optimality Conditions in Differentiable Multiobjective Programming. Journal of Optimization Theory and Applications 109, 187–192 (2001). https://doi.org/10.1023/A:1017570023018
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DOI: https://doi.org/10.1023/A:1017570023018