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Sufficiency and duality in non-smooth interval valued programming problems. (English) Zbl 1438.90336

Summary: In this paper a non-smooth optimization problem is studied in an uncertain environment. The objective function of this problem is interval valued function. We introduce the class of \(LU-(p, r)-[\rho^L, \rho^U]-(\eta, \theta)\)-invex interval valued functions about the Clarke generalized gradient. Then, through non trivial examples, we illustrate that the class of functions introduced exists. Based upon the proposed invexity assumptions, the sufficient optimality conditions are established. Further, we derive weak, strong and strict converse duality theorems for Mond-Weir type and Wolfe type dual programs. Some examples are also given in order to illustrate our results.

MSC:

90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)
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