Optimization and Differentiation

"The book under review provides an inspired presentation of the tools offered by mathematical analysis and its derivatives" such as variational calculus and optimal control theory in solving extremal problems [...] This clearly written book will be useful for researches as well as students willing to enter in the field."

-Gheorghe Anicul?aesei, Zentralblatt MATH

"This book provides an inspired presentation of tools o?ered by mathematical analysis and used in variational calculus of variations and optimal control theory, for solving extremal problems. This clearly written book will be useful for researchers as well as students interested in entering the ?eld.

The main topics considered in the monograph are as follows: Part I: Minimization of Functionals: necessary conditions of extremum for functionals; Part II: Stationary Systems: linear stationary systems, weakly nonlinear stationary systems, strongly non-linear stationary systems, stationary systems with the coe?cient control, stationary systems with nonlinear control; Part III: Evolutional Systems: ?rst-order linear evo-lutional systems, ?rst-order nonlinear evolutional systems, second-order evolutional systems, Navier-Stokes equations; Part IV: Addition: functors of the di?erentiation.
In the last part, the author interprets di?erentiation by using category theory and in particular proposes a concept of extended derivation of an operator. By means of this notion, necessary conditions of optimality are obtained."

-Angelo Favini - Mathematical Reviews Clippings - November 2018