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... The equilibrium point xeq 2 Rn is (Lyapunov) stable if 9 a 2 K: ||x(t) – xeq|| · a(||x(t0) – xeq||) 8 t¸ t0¸ 0, ||x(t0) – xeq||· c Theorem (Lyapunov): Suppose there exists a continuously differentiable, positive definite, radially unbounded function V: Rn ! R such that Then xeq is a Lyapunov stable ...
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Mathematical optimization



In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding ""best available"" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.
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