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Full-Text Articles in Physical Sciences and Mathematics
Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka
Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka
Wayne State University Dissertations
Bilevel programming problems are of growing interest both from theoretical and practical points of view. These models are used in various applications, such as economic planning, network design, and so on. The purpose of this dissertation is to study the pessimistic (or strong) version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation developed by B. Mordukhovich.
This dissertation begins with analyzing pessimistic bilevel programs, formulation of the problems, literature review, practical application, existence of …
Variational Analysis In Parametric Optimization, Yen Nhi Nguyen Thi
Variational Analysis In Parametric Optimization, Yen Nhi Nguyen Thi
Wayne State University Dissertations
The dissertation is devoted to the development of variational analysis and generalized differentiation in infinite dimensions. We derive new calculus rules for both first-order partial subdifferentials and second-order partial subdifferentials in the framework of general Banach spaces as well as more developed rules in the framework of Asplund spaces. This calculus is applied in the study of sensitivity analysis for solution maps to the parameterized generalized equations in Asplund spaces, where both bases and fields are parameter-dependent multifunctions. We analyze the parametric sensitivity of either stationary points or stationary point multiplier multifunctions associated with parameterized optimization problems under consideration. The …
Asymptotic Properties Of Markov Modulated Sequences With Fast And Slow Time Scales, Son Luu Nguyen
Asymptotic Properties Of Markov Modulated Sequences With Fast And Slow Time Scales, Son Luu Nguyen
Wayne State University Dissertations
In this dissertation we investigate asymptotic properties of Markov modulated random processes having two-time scales. The model contains a number of mixing sequences modulated by a switching process that is a discrete-time Markov chain. The motivation of our study stems from applications in manufacturing systems, communication networks, and economic systems, in which regime-switching models are used.
This thesis focuses on asymptotic properties of the Markov modulated processes under suitable scaling. Our main effort focuses on obtaining weak convergence and strong approximation results.