Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity.

This paper focuses on a nonsmooth nonconvex interval-valued optimization problem. For this, we propose interval-valued symmetric invexity, interval-valued symmetric pseudo-invexity and interval-valued symmetric quasi-invexity in terms of the symmetric gH-differentiable interval-valued functions. Some important properties of these generalized convexities are also discussed. By utilizing these new concepts, we establish sufficient Karush–Kuhn–Tucker conditions for the considered problem. Further, the Wolfe and Mond–Weir type dual problems are associated and weak, strong and strict converse duality results have been derived. Finally, we apply the developed theory to a binary classification problem of interval data by support vector machine. • Generalized convexities were proposed using the symmetric gH-derivative. • Some important properties of these generalized convexities were also discussed. • Sufficient KKT conditions for the NIVOPs were established. • The dual problems were associated and duality results had been derived. [ABSTRACT FROM AUTHOR]