The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.
The paper contributes the first logical analysis of the problems solved in the theorems 2.1, 2.2 (optimization in kinematics), 3.3 (minimization of the total cost), Lemma 4.2 (approximation), Theorem 4.3 (solving the moment problem). The paper’s primary contribution is finding that suitable polynomial approximation yields solving the multidimensional moment problem. This study documents how practical and theoretical problems can be solved.
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