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A Regularization Technique In Dynamic Optimization, Alvaro Guevara
A Regularization Technique In Dynamic Optimization, Alvaro Guevara
LSU Doctoral Dissertations
In this dissertation we discuss certain aspects of a parametric regularization technique which is based on recent work by R. Goebel. For proper, lower semicontinuous, and convex functions, this regularization is self-dual with respect to convex conjugation, and a simple extension of this smoothing exhibits the same feature when applied to proper, closed, and saddle functions. In Chapter 1 we give a introduction to convex and saddle function theory, which includes new results on the convergence of saddle function values that were not previously available in the form presented. In Chapter 2, we define the regularization and extend some of …
Dynamical Systems With Time Delay, Norma Ortiz
Dynamical Systems With Time Delay, Norma Ortiz
LSU Doctoral Dissertations
In this dissertation, we study necessary conditions and weak invariance properties of dynamical systems with time delay. A number of results have been obtained recently that refine necessary conditions of optimal solutions for nonsmooth dynamical systems without time delay. In this dissertation, we examine the extension of some of these results to problems with time delay. In particular, we study the generalized problem of Bolza with the addition of delay in the state and velocity variables and refer to this problem as the Neutral Problem of Bolza. We consider the relationship between the generalized problem of Bolza with time delay …