Abstract
In this paper, we introduce the concepts of invexity, quasi-invexity and pseudo-invexity for interval-valued functions in parametric form. Sufficient optimality conditions for a class of interval-valued optimization problems are derived for feasible solution to be an efficient solution under proposed invexity assumptions. Furthermore, we formulate Wolfe and Mond–Weir type duals and establish appropriate duality theorems in order to relate the efficient solutions of primal and dual programs. Some examples are also constructed to illustrate the proposed invexity and weak duality theorems.
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The authors thank the anonymous reviewers for their valuable comments which help to improve the quality of the paper.
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This research is financially supported by Department of Science and Technology, New Delhi, India through Grant No. SR/FTP/MS-007/2011.
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Jayswal, A., Stancu-Minasian, I., Banerjee, J. et al. Sufficiency and duality for optimization problems involving interval-valued invex functions in parametric form. Oper Res Int J 15, 137–161 (2015). https://doi.org/10.1007/s12351-015-0172-2
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DOI: https://doi.org/10.1007/s12351-015-0172-2