Applied Mathematics Commons^™

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 …

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 …