Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In convex analysis and the calculus of variations, branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minimima, but need not actually be convex. Informally, a differentiable function is pseudoconvex if it is increasing in any direction where it has a positive directional derivative. Every convex function is pseudoconvex, but the converse is not true. For example, the function (x) = x + x3 is pseudoconvex but not convex. Any pseudoconvex function is quasiconvex, but the converse is not true since the function (x) = x3 is quasiconvex but not pseudoconvex. A pseudoconcave function is a function whose negative is pseudoconvex. A pseudolinear function is a function that is both pseudoconvex and pseudoconcave.

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