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Full-Text Articles in Physical Sciences and Mathematics
Second-Order Generalized Differentiation Of Piecewise Linear-Quadratic Functions And Its Applications, Hong Do
Wayne State University Dissertations
The area of second-order variational analysis has been rapidly developing during the recent years with many important applications in optimization. This dissertation is devoted to the study and applications of the second-order generalized differentiation of a remarkable
class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to optimization and stability.
The first goal of this dissertation is to compute the second-order subdifferential of the functions described above, which will be applied in the study of the stability of composite optimization problems associated with piecewise linear-quadratic functions, known as extended …
Optimal Control Of A Perturbed Sweeping Process With Applications To The Crowd Motion Model, Tan Hoang Cao
Optimal Control Of A Perturbed Sweeping Process With Applications To The Crowd Motion Model, Tan Hoang Cao
Wayne State University Dissertations
The dissertation is devoted to the study and applications of a new class of optimal control problems governed by a perturbed sweeping process of the hysteresis type with control functions acting in both play-and-stop operator and additive perturbations. Such control problems can be reduced to optimization of discontinuous and unbounded dif- ferential inclusions with pointwise state constraints, which are immensely challenging in control theory and prevent employing conventional variation techniques to derive neces- sary optimality conditions. We develop the method of discrete approximations married with appropriate generalized differential tools of modern variational analysis to overcome principal difficulties in passing to …