Abstract
The present paper provides first and second-order characterizations of a radially lower semicontinuous strictly pseudoconvex function ƒ : X → ℝ defined on a convex set X in the real Euclidean space ℝ n in terms of the lower Dini-directional derivative. In particular we obtain connections between the strictly pseudoconvex functions, nonlinear programming problem, Stampacchia variational inequality, and strict Minty variational inequality. We extend to the radially continuous functions the characterization due to Diewert, Avriel, Zang [J. Econom. Theory 25: 397–420, 1981]. A new implication appears in our conditions. Connections with other classes of functions are also derived.
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