# Pseudoconvex Function

### Overview

High Quality Content by WIKIPEDIA articles! 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 ƒ(x) = x + x3...
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### Overview

High Quality Content by WIKIPEDIA articles! 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 ƒ(x) = x + x3 is pseudoconvex but not convex. Any pseudoconvex function is quasiconvex, but the converse is not true since the function ƒ(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.

### Product Details

• ISBN-13: 9786134714426
• Publisher: Betascript Publishing
• Publication date: 12/30/2010
• Pages: 124
• Product dimensions: 0.29 (w) x 9.00 (h) x 6.00 (d)

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