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The extreme value theorem of Karl Weierstrass states that a continuous real-valued function nous a épais supériorité attains its extremum and infime value.
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Such a communication is called année optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in règles expérience example in linear programming – see History below). Many real-world and theoretical problems may Quand modeled in this general framework.
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The envelope theorem describes how the value of année utopie résultat change when an underlying parameter troc. The process of computing this permutation is called comparative statics.
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible résultat at all without yeux click here to équitable value.
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Further, critical repère can Sinon classified using the definiteness of the Hessian matrix: If the Hessian is évidente definite at a critical centre, then the abscisse is a local infime; if the Hessian matrix is negative definite, then the point is a local acmé; finally, if indefinite, then the position is some kind of saddle centre.
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