Optimization and Differentiation
Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.
Minimization of the Functionals. Necessary Conditions of the Functional Extremum. Minimization of the Functionals. Stationary Systems. Linear Stationary Systems. Weak Nonlinear Stationary Systems. Strong Nonlinear Stationary Systems. Stationary Systems with the Coefficient Control. Stationary Systems with Nonlinear Control. Evolutional Systems. First Order Linear Evolutional Systems. First Order Nonlinear Evolutional Systems. Second Order Evolutional Systems. Navier – Stokes equations. Additions. Optimal Control Problems with the Different State Equations. Optimal Control Problems with Different Controls. Optimal Control Problems with the Different State Functionals. Optimal Control Problems with Different Constraints. Appendix. Differentiation, Optimization and Categories Theory. Elementary Conterexamples of the Optimization Control Theory.
"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 oﬀered 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 ﬁeld.
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 coeﬃcient control, stationary systems with nonlinear control; Part III: Evolutional Systems: ﬁrst-order linear evo-lutional systems, ﬁrst-order nonlinear evolutional systems, second-order evolutional systems, Navier-Stokes equations; Part IV: Addition: functors of the diﬀerentiation.
In the last part, the author interprets diﬀerentiation 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