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Graduate Program Director Manual

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Graduate Program Director Manual

Portland state UniversityPDXScholarDissertations and ThesesDissertations and ThesesSpring 6-1-2017Generalized Differential Calculus and Applications t

Graduate Program Director ManualtoOptimizationR. Blake RectorPortland State UniversityFollow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etdsÔ1 Part

of the Mathematics Commons, and the Power and Energy CommonsLet us know how access to this document benefits you.Recommended CitationRector, R Blake, Graduate Program Director Manual

'Generalized Differential Calculus and Applications to Optimization" (2017). Dissertations and Theses. Paper 3627.https://doi org/10.15760/etd.5519Thi

Graduate Program Director Manual

s Dissertation is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrat

Portland state UniversityPDXScholarDissertations and ThesesDissertations and ThesesSpring 6-1-2017Generalized Differential Calculus and Applications t

Graduate Program Director Manuall Calculus and Applications to OptimizationbyRobert Blake Hayden RectorA dissertation submitted in partial fulfillment of the requirements for the deg

ree ofDoctor of Philosophy inMat hematical SciencesDissert at ion Commit t ee: Mau Nam Nguyen, Chair Robert Bass Gerardo Lalferrierc Bin .Jiang Tugrul Graduate Program Director Manual

DaiuiPortland State University2017(c) 2017 Robert Blake Hayden RectorAbstractThis thesis cont ains contributions in three areas: the t heory of gener

Graduate Program Director Manual

alized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geomet

Portland state UniversityPDXScholarDissertations and ThesesDissertations and ThesesSpring 6-1-2017Generalized Differential Calculus and Applications t

Graduate Program Director Manualcifically pert ain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valuer! map

s, called the coderivative, in infinite dimensions. A strong understanding of the subdiiferential is essent ial for numerical optimization algorit hms Graduate Program Director Manual

, which are developed and applied to nonsmoot h problems in operations research, including non-convex problems. Finally, an optimization framework is

Graduate Program Director Manual

applied to solve a problem in elect ric power systems involving a smart solar inverter and battery storage system providing energy ami ancillary servi

Portland state UniversityPDXScholarDissertations and ThesesDissertations and ThesesSpring 6-1-2017Generalized Differential Calculus and Applications t

Graduate Program Director Manual mathematics.iiTable of ContentsAbstract................................................................ i

Portland state UniversityPDXScholarDissertations and ThesesDissertations and ThesesSpring 6-1-2017Generalized Differential Calculus and Applications t

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