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Providing Better Choices: An Exploration Of Solutions In Multi-Objective Optimization And Game Theory Using Variational Analysis, Glenn Matthew Harris

Graduate Research Theses & Dissertations

Multi-objective optimization problems and game theory problems have a wide array of

applications and because of this there are different types of solutions available. This dissertation

explores two areas of optimization and a solution type for each. First, substantial

efficiency (SE) as a type of solution to multi-objective optimization problems that extends

proper efficiency. Secondly, strong Nash equilibria (SNE) as a type of solution to game

theoretic problems that extends Nash equilibria. Substantial efficiency is demonstrated to

be a superior solution to the more rudimentary notion of proper efficiency in solving some

multi-objective financial market and economic problems. Using this …

A Spider's Web Of Doughnuts, Daniel Stoertz

Graduate Research Theses & Dissertations

This dissertation studies an interplay between the dynamics of iterated quasiregular map-

pings and certain topological structures. In particular, the relationship between the Julia set

of a uniformly quasiregular mapping f : R 3 → R 3 and the fast escaping set of its associated

Poincaré linearizer is explored. It is shown that, if the former is a Cantor set, then the latter

is a spider’s web. A new class of uniformly quasiregular maps is constructed to which this

result applies. Toward this, a geometrically self-similar Cantor set of genus 2 is constructed.

It is also shown that for any …

The Effect Of Self-Reflection On Relative Student Success In Undergraduate Calculus 1, Kevin Shryock

Graduate Research Theses & Dissertations

This thesis examines the effect of completion and self-reflection credit on multiple aspects of undergraduate student success in Calculus 1. Specifically, this study assessed the validity of a plug-and-play classroom framework utilizing a combination of a holistic rubric and corresponding worksheets to direct students’ attention towards their conceptual understanding of material and written work, all while removing the pressure of performance grades on all but four summative assessments. By comparing students’ relative performance on these summative assessments, as well as students’ responses on regular surveys, this study found that students who chose to forego performance grades in favor of completion …

Projective Splitting Methods For Maximal Monotone Mappings In Hilbert Spaces, Oday Hazaimah

Graduate Research Theses & Dissertations

In this dissertation, novel approaches for solving convex nonsmooth optimization, variational inequalities and inclusion problems are studied. The main contributions of the dissertation are given in Chapter 4 and Chapter 5. The two proposed iterations in Chapter 4, Half-Extragradient algorithm (HEG) and its accelerated version, are a natural modification of the classical Extragradient algorithm (EG)

when the composite objective function is a sum of three convex functions. EG evaluates the smooth operator twice per iteration via proximal mappings, and also, it allows larger step sizes. One of the main advantages of the proposed scheme is to avoid evaluating an

extragradient …

A Computational Study Of Binary Linear And Quadratic Programming And Solvers, William Cody Mackelfresh

Graduate Research Theses & Dissertations

In this thesis we study and compare computational capability of two solvers, Gurobi and BiqCrunch, and their capabilities to solve various binary quadratic and linear programming problems. We review two types of programming models for three types of combinatorial optimization problems, namely Max-Cut, Max Independent Set, and Max-$k$-Cluster. We also review the Reformulation-Linearization Technique (RLT) and Semidefinite Programming (SDP) approaches for solving these models, go over the software and hardware used to solve these problems, and finally review the numerical results obtained by solving the problems.