Sökning: "convex analysis"
Visar resultat 1 - 5 av 100 avhandlingar innehållade orden convex analysis.
1. Convexity, Currents, and Lelong numbers
Sammanfattning : This thesis treats different aspects of convexity, both real and complex. On the real side, we study convexity in relation with certain currents. On the complex side, we study the singularities of plurisubharmonic functions. LÄS MER
2. Asynchronous First-Order Algorithms for Large-Scale Optimization : Analysis and Implementation
Sammanfattning : Developments in communication and data storage technologies have made large-scale data collection more accessible than ever. The transformation of this data into insight or decisions typically involves solving numerical optimization problems. LÄS MER
3. Positive vector bundles in complex and convex geometry
Sammanfattning : This thesis concerns various aspects of the geometry of holomorphic vector bundles and their analytical theory which all, vaguely speaking, are related to the notion of positive curvature in general, and L^2-methods for the dbar-equation in particular. The thesis contains four papers. LÄS MER
4. Minkowski Measure of Asymmetry and Minkowski Distance for Convex Bodies
Sammanfattning : This thesis consists of four papers about the Minkowski measure of asymmetry and the Minkowski (or Banach-Mazur) distance for convex bodies.We relate these two quantities by giving estimates for the Minkowski distance in terms of the Minkowski measure. LÄS MER
5. Non-Convex Methods for Compressed Sensing and Low-Rank Matrix Problems
Sammanfattning : In this thesis we study functionals of the type \( \mathcal{K}_{f,A,\b}(\x)= \mathcal{Q}(f)(\x) + \|A\x - \b \| ^2 \), where \(A\) is a linear map, \(\b\) a measurements vector and \( \mathcal{Q} \) is a functional transform called \emph{quadratic envelope}; this object is a very close relative of the \emph{Lasry-Lions envelope} and its use is meant to regularize the functionals \(f\). Carlsson and Olsson investigated in earlier works the connections between the functionals \( \mathcal{K}_{f,A,\b}\) and their unregularized counterparts \(f(\x) + \|A\x - \b \| ^2 \). LÄS MER