Lesson plan
Global optimization
Global optimization is a branch of operations research, applied mathematics, and numerical analysis that attempts to find the global minimum or maximum 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 equivalent to the minimization of the function f(x):=(-1)\cdot g(x) . Given a possibly nonlinear and non-convex continuous function f:\Omega\subset\mathbb{R}^n\to\mathbb{R} with the global minimum f^* and the set of all global minimizers X^* in \Omega , the standard minimization problem can be given as : \min_{x\in\Omega}f(x), that is, finding f^* and a global minimizer in X^* ; where \Omega is a (not necessarily convex) compact set defined by inequalities g_i(x)\geqslant0, i=1,\ldots,r . Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding local minima or maxima. Finding an arbitrary local minimum is relatively straightforward by using classical local optimization methods. Finding the global minimum of a function is far more difficult: analytical methods are frequently not applicable, and the use of numerical solution strategies often leads to very hard challenges.
Article summary
Global optimization is a branch of operations research, applied mathematics, and numerical analysis that attempts to find the global minimum or maximum 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 equivalent to the minimization of the function f(x):=(-1)\cdot g(x) . Given a possibly nonlinear and non-convex continuous function f:\Omega\subset\mathbb{R}^n\to\mathbb{R} with the global minimum f^* and the set of all global minimizers X^* in \Omega , the standard minimization problem can be given as : \min_{x\in\Omega}f(x), that is, finding f^* and a global minimizer in X^* ; where \Omega is a (not necessarily convex) compact set defined by inequalities g_i(x)\geqslant0, i=1,\ldots,r . Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding local minima or maxima. Finding an arbitrary local minimum is relatively straightforward by using classical local optimization methods. Finding the global minimum of a function is far more difficult: analytical methods are frequently not applicable, and the use of numerical solution strategies often leads to very hard challenges.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.