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Nonconvex functions and variational inequalities

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Abstract

In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and arc-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia

    M. A. Noor (Professor)

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  1. M. A. Noor
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Communicated by F. Giannessi

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Noor, M.A. Nonconvex functions and variational inequalities. J Optim Theory Appl 87, 615–630 (1995). https://doi.org/10.1007/BF02192137

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