Titlebook: Economists‘ Mathematical Manual; Knut Syds?ter,Arne Str?m,Peter Berck Textbook 2005Latest edition Springer-Verlag Berlin Heidelberg 2005 S

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Linear and nonlinear programming,If either of the problems (15.1) and (15.2) has a finite optimal solution, so has the other, and the corresponding values of the objective functions are equal. If either problem has an “unbounded optimum”, then the other problem has no admissible solutions.

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Calculus of variations and optimal control theory,The .. A necessary condition for the solution of (16.1). An alternative form of the Euler equation. The .. A necessary condition for the solution of (16.1). Sufficient conditions for the solution of (16.1). . Adding condition (16.5) gives sufficient conditions.

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,Vectors in ?,. Abstract spaces,Definition of a linear combination of vectors. Definition of linear dependence and independence. A characterization of linear independence for . vectors in ?.. (See (19.23) for the definition of rank.) A characterization of linear independence for . vectors in ?.. (A special case of (18.4).)

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