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Название: Mathematical Programming and Control Theory
Автор: Craven B.D.
This book presents a unified theory of nonlinear mathematical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e.g. a continuous curve (i.e. infinitely many variables). The underlying ideas of vector space, convex cone, and separating hyperplane are the same, whether the dimension is finite or infinite; and infinite dimension makes very little difference to the proofs. Duality theory - the various nonlinear generalizations of the well-known duality theorem of linear programming - is found relevant also to optimal control, and thePontryagin theory for optimal control also illuminates finite dimensional problems. The theory is simplified, and its applicability extended, by using the geometric concept of convex cones, in place of coordinate inequalities.