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Chapter 4

Fundamentals of Optimization

4.1 Definition and Classification

4.1.1 Definitions in the Optimization Problem

Optimization is an important tool in decision science and in the analysis of physical systems . In a mathematical framework, optimization is the minimization or maximization of a function subject to constraints on its variables. The optimization problem can be formulated as following :

(4.1) where is the vector of variables, which depends on certain characteristics of the system. is the objective function (or cost function), a scalar function of that is to be maximized or minimized. are scalar constraint functions, of which define certain equations and inequalities that the variable vector must satisfy. The set of satisfying all the constraints are referred to ...

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