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In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an -optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) -convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) -optimal solutions of the multi-dimensional...
The purpose of this paper is to apply second order -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order -saddle point and the second order -Lagrange function are defined for the second order -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the...
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