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Nonconvex Function

Let D be a convex set in a real vector space. A function f:D->R is nonconvex if it is not a convex function; equivalently, there are x,y in D and 0<t<1 such that

f(tx+(1-t)y)>tf(x)+(1-t)f(y).

A nonconvex function can have multiple local minima, so a local optimization method need not find a global minimum.

See also

Convex Function, Convex Set, Global Minimum, Local Minimum, Optimization Theory

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References

Boyd, S. and Vandenberghe, L. Convex Optimization. Cambridge, England: Cambridge University Press, 2004. https://web.stanford.edu/~boyd/cvxbook/.

Cite this as:

Weisstein, Eric W. "Nonconvex Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonconvexFunction.html

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