Nonconvex functions and variational inequalities |
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Authors: | M. A. Noor |
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Affiliation: | (1) Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia |
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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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Keywords: | Nonconvex functions semipreinvex functions semi-invex sets variational-like inequalities iterative algorithms |
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