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Optimal Control of Distributed Systems with Conjugation Conditions. Authors; ( view affiliations). Ivan V. Sergienko; Vasyl S. Deineka. Editors; (view affiliations). This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and.
Numerical Functional Analysis and Optimization 32 :2, Natural Science 03 , Applied Mathematics 02 , IMF Working Papers 11 , 1. Computational Lithography, Applied Mathematics and Computation :5, Numerical Functional Analysis and Optimization 31 :8, Journal of Computational and Applied Mathematics :5, Numerische Mathematik :1, Nonlinear Analysis: Real World Applications 11 :3, Journal of Interdisciplinary Mathematics 13 :3, Journal of Computational and Applied Mathematics :2, Numerical Algorithms 54 :1, Computing 87 , SIAM Review 52 :1, Journal of Software Engineering and Applications 03 , Numerical Algorithms 53 :1, Applied Mathematics and Computation :6, Applied Mathematics and Computation :2, Journal of the Korean Statistical Society 38 :1, I have emphasized more from the very beginning the fundamental importance of the concepts of Lagrangian function, saddle-point and saddle-value.
Instead of first outlining everything relevant about conjugate convex functions and then deriving its consequences for optimization, I have tried to introduce areas of basic theory only as they became needed and their significance for the study of dual problems more apparent. In particular, general results on the calculation of conjugate functions have been postponed nearly to the end. I have also attempted to show just where it is that convexity is needed, and what remains true if certain convexity or lower-semicontinuity assumptions are dropped.
The notation and terminology of  have been changed somewhat to make an easier introduction to the subject. The duality theorem for linear programming problems, for instance, turns out to be an analogue of an algebraic identity relating a linear transformation and its adjoint. For more on this point of view and its possible fertility for applications such as to mathematical economics, see .
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Add to my favorites. We have a dedicated site for Germany. Authors: Sergienko , Ivan V. This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, pseudoparabolic, hyperbolic, and pseudohyperbolic equations and with elasticity theory equation systems that have nonsmooth solutions, including discontinuous solutions.
With the basis of this methodology, the monograph shows a continuous dependence of states, namely, of solutions to the enumerated boundary-value and initial boundary-value problems including discontinuous states and a dependence of solution traces on distributed controls and controls at sectors of n -dimensional domain boundaries and at n—1 -dimensional function-state discontinuity surfaces i.
Such an aspect provides the existence of optimal controls for the mentioned systems with J. Besides this, the authors consider some new systems, for instance, the ones described by the conditionally correct Neumann problems with unique states on convex sets, and such states admit first-order discontinuities.
These systems are also described by quartic equations with conjugation conditions, by parabolic equations with constraints that contain first-order time state derivatives in the presence of concentrated heat capacity, and by elasticity theory equations. In a number of cases, when a set of feasible controls coincides with corresponding Hilbert spaces, the authors propose to use the computational algorithms for the finite-element method.