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    • Algorithms for structured nonconvex optimization: theory and practice 

      Nguyen, Hieu Thao (2018-07-24)
      We first synthesize and unify notions of regularity, both of individual functions/sets and of families of functions/sets, as they appear in the convergence theory of fixed point iterations. Several new primal and dual ...
    • Fixed Point Algorithms for Nonconvex Feasibility with Applications 

      Hesse, Robert (2014-07-31)
      Projection algorithms for solving (nonconvex) feasibility problems provide powerful and computationally efficient schemes for a wide variety of applications. Algorithms as Alternating Projections (AP) and Douglas-Rachford ...
    • Investigations in Hadamard spaces 

      Bërdëllima, Arian (2021-08-27)
      This thesis investigates the interplay between geometry and convex analysis in Hadamard spaces. Motivated by numerous applications of CAT(0) geometry, our work builds upon the results in convex analysis and Alexandrov ...
    • Projection Methods in Sparse and Low Rank Feasibility 

      Neumann, Patrick (2015-07-07)
      In this thesis, we give an analysis of fixed point algorithms involving projections onto closed, not necessarily convex, subsets of finite dimensional vector spaces. These methods are used in applications such as imaging ...
    • Random Function Iterations for Stochastic Feasibility Problems 

      Hermer, Neal (2019-03-21)
      The aim of this thesis is to develop a theory that describes errors in fixed point iterations stochastically, treating the iterations as a Markov chain and analyzing them for convergence in distribution. These particular ...
    • Variational Regularization Strategy for Atmospheric Tomography 

      Altuntac, Erdem (2016-07-22)
      The main focus of this dissertation is to establish the necessary theory with numerical illustrations for solving an atmospheric tomography problem. The inverse problem is the reconstruction of some volume data ...