Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Asymptotic expansion (1)
- Collocation, Geometric, Runge-Kutta, Supergeometric, Weakly Singular (1)
- Discrete approximations (1)
- Dissipative differential inclusions (1)
- Extremal principles (1)
-
- Generalized differentiation (1)
- Generating (1)
- Genus (1)
- Groups (1)
- Hybrid systems (1)
- Manifolds (1)
- Morse Theory (1)
- Multiobjective optimization (1)
- Newton's method (1)
- Optimal control (1)
- Semi-infinite programming (1)
- Singular system (1)
- Stability (1)
- Sweeping process (1)
- System of backward equation (1)
- Topology (1)
- Two-time scale (1)
- Variational analysis (1)
Articles 1 - 7 of 7
Full-Text Articles in Entire DC Network
Variational Analysis And Optimal Control Of The Sweeping Process, Hoang Dinh Nguyen
Variational Analysis And Optimal Control Of The Sweeping Process, Hoang Dinh Nguyen
Wayne State University Dissertations
We formulate and study an optimal control problem for the sweeping(Moreau) process, where control functions enter the moving sweeping
set. To the best of our knowledge, this is the first study in the literature devoted to optimal control of the sweeping process. We first establish an existence theorem of optimal solutions and then derive necessary optimality conditions for this optimal control problem of a new type, where the dynamics is governed by discontinuous differential inclusions with variable right-hand sides. Our approach to necessary optimality conditions is based on the method of discrete approximations and advanced tools of variational analysis and …
Spectral Collocation Method For Compact Integral Operators, Can Huang
Spectral Collocation Method For Compact Integral Operators, Can Huang
Wayne State University Dissertations
We propose and analyze a spectral collocation method for integral
equations with compact kernels, e.g. piecewise smooth kernels and
weakly singular kernels of the form $\frac{1}{|t-s|^\mu}, \;
0<\mu<1. $ We prove that 1) for integral equations, the convergence
rate depends on the smoothness of true solutions $y(t)$. If $y(t)$
satisfies condition (R): $\|y^{(k)}\|_{L^\infty[0,T]}\leq
ck!R^{-k}$}, we obtain a geometric rate of convergence; if $y(t)$
satisfies condition (M): $\|y^{(k)}\|_{L^{\infty}[0,T]}\leq cM^k $,
we obtain supergeometric rate of convergence for both Volterra
equations and Fredholm equations and related integro differential
equations; 2) for eigenvalue problems, the convergence rate depends
on the smoothness of eigenfunctions. The same convergence rate for
the largest modulus eigenvalue approximation …
\mu<1.>Genus 0, 1, 2 Actions Of Some Almost Simple Groups Of Lie Rank 2, Xianfen Kong
Genus 0, 1, 2 Actions Of Some Almost Simple Groups Of Lie Rank 2, Xianfen Kong
Wayne State University Dissertations
Please see the paper.
Thanks.
New Variational Principles With Applications To Optimization Theory And Algorithms, Hung Minh Phan
New Variational Principles With Applications To Optimization Theory And Algorithms, Hung Minh Phan
Wayne State University Dissertations
In this dissertation we investigate some applications of variational analysis in optimization theory and algorithms. In the first part we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, under the name of tangential extremal principles and rated extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. These developments are in the core geometric theory of variational analysis. Our study includes the basic theory and applications to problems of semi-infinite programming …
Numerical Methods For Problems Arising In Risk Management And Insurance, Zhuo Jin
Numerical Methods For Problems Arising In Risk Management And Insurance, Zhuo Jin
Wayne State University Dissertations
In this dissertation we investigate numerical methods for problems annuity purchasing and dividend optimization arising in risk management and insurance. We consider the models with Markov regime-switching process. The regime-switching model contains both continuous and discrete components in their evolution and is referred to as a hybrid system. The discrete events are used to model the random factors that cannot formulated by differential equations. The switching process between regimes is modulated as a finite state Markov chain.
As is widely recognized, this regime-switching model appears to be more versatile and more realistic. However, because of the regime switching and the …
Asymptotic Expansions And Stability Of Hybrid Systems With Two-Time Scales, Dung Tien Nguyen
Asymptotic Expansions And Stability Of Hybrid Systems With Two-Time Scales, Dung Tien Nguyen
Wayne State University Dissertations
In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One
of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.
In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has …
Moduli Spaces And Cw Structures Arising From Morse Theory, Lizhen Qin
Moduli Spaces And Cw Structures Arising From Morse Theory, Lizhen Qin
Wayne State University Dissertations
In this dissertation, we study the moduli spaces and CW Structures arising from Morse theory.
Suppose M is a smooth manifold and f is a Morse function on it. We consider the negative gradient flow of f. Suppose the flow satisfies transversality. This naturally defines the moduli spaces of flow lines and gives a stratication of M by its unstable manifolds. The gluing of broken flow lines can also be constructed.
We prove that, under certain assumptions, these moduli spaces can be compactified and the compactified spaces are smooth manifolds with corners. Moreover, these compactified manifolds satisfy certain orientation formulas. …