Physical description 
1 online resource (212 pages). 
Series 
Mathematics and Its Applications ; 431 

Mathematics and Its Applications ; 431.

Summary 
This monograph is the first book in the study of necessary conditions of an extremum in which topological connectedness plays a major role. Many new and original results are presented here. The synthesis of the wellknown DybrovitskiiMilyutin approach, based on functional analysis, and topological methods permits the derivation of the socalled alternative conditions of an extremum: if the Euler equation has the trivial solution only at an extreme point, then some inclusion is valid for the functionals belonging to the dual space. Also, the present approach gives a transparent answer to the question why the KuhnTucker theorem establishes the restrictions on the signs of the Lagrange multipliers for the inequality constraints but why this theorem does not establish any analogous restrictions on the multipliers for the equality constraints. Examples from mathematical economics illustrate the alternative conditions of any extremum. Parallels are drawn between these examples and the problems of static equilibrium in classical mechanics. Audience: This volume will be of use to mathematicians and graduate students interested in the areas of optimization, optimal control and mathematical economics. 
Subject 
Mathematics.


Discrete groups.


Mathematical optimization.


Topology.


Economics.


Electronic books. 
ISBN 
9789401591195 (electronic bk.) 

9401591199 (electronic bk.) 

9789048149810 

9048149819 

9401591199 
