642 results about "Global optimization" patented technology

Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function g(x) is obviously equivalent to the minimization of the function f(x):=(-1)·g(x). Given a possibly nonlinear and non-convex continuous function f:Ω⊂ℝⁿ→ℝ with the global minima f* and the set of all global minimizers X* in Ω, the standard minimization problem can be given as minₓ∈Ωf(x), that is, finding f* and a global minimizer in X*; where Ω is a (not necessarily convex) compact set defined by inequalities gᵢ(x)⩾0,i=1,…,r.