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Nahak, C.; Mohapatra, R. N.

\(d-\rho -(\eta ,\theta )\)-invexity in multiobjective optimization. (English) Zbl 1155.90451

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 6, 2288-2296 (2009).
Summary: A generalization of convexity is considered in the case of multiobjective optimization problems, where the functions involved are non-differentiable. Under \(d-\rho -(\eta ,\theta )\)-invexity assumptions on the functions involved, weak, strong and converse duality results are proved to relate weak Pareto (efficient) solutions of the multiobjective programming problems (PVP),(DVP) and (MWD). We have also established the Karush-Kuhn-Tucker sufficient optimality condition.

Cited in 8 Documents

MSC:

90C29 Multi-objective and goal programming
26B25 Convexity of real functions of several variables, generalizations
49N15 Duality theory (optimization)

Keywords:

multiobjective problem; \(d-\rho -(\eta, \theta )\)-invexity; efficiency; proper efficiency; duality
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\textit{C. Nahak} and \textit{R. N. Mohapatra}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 6, 2288--2296 (2009; Zbl 1155.90451)
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