A Hybrid Semismooth Quasi-Newton Method Part 2: Applications

[1]  Juan Carlos De Los Reyes,et al.  Numerical PDE-Constrained Optimization , 2015 .

[2]  Wilson Fong Handbook of MRI Pulse Sequences , 2005 .

[3]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[4]  Kawin Setsompop,et al.  Advancing RF pulse design using an open‐competition format: Report from the 2015 ISMRM challenge , 2017, Magnetic resonance in medicine.

[5]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[6]  Mikhail V. Solodov,et al.  Merit functions and error bounds for generalized variational inequalities , 2003 .

[7]  Amir Beck,et al.  First-Order Methods in Optimization , 2017 .

[8]  J. Pauly,et al.  Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm [NMR imaging]. , 1991, IEEE transactions on medical imaging.

[9]  P. Anselone,et al.  Collectively Compact Operator Approximation Theory and Applications to Integral Equations , 1971 .

[10]  Jorge Nocedal,et al.  Representations of quasi-Newton matrices and their use in limited memory methods , 1994, Math. Program..

[11]  K. Kunisch,et al.  Total variation regularization of multi-material topology optimization , 2017, 1708.06165.

[12]  P. Philip Optimal Control of Partial Dierential Equations , 2013 .

[13]  Jessika Eichel,et al.  Collectively Compact Operator Approximation Theory And Applications To Integral Equations , 2016 .

[14]  Anton Schiela A Simplified Approach to Semismooth Newton Methods in Function Space , 2008, SIAM J. Optim..

[15]  Karl Kunisch,et al.  Simultaneous multislice refocusing via time optimal control , 2018, Magnetic resonance in medicine.

[16]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

[17]  Kazufumi Ito,et al.  Lagrange multiplier approach to variational problems and applications , 2008, Advances in design and control.

[18]  Mircea Sofonea,et al.  Elements of Nonlinear Analysis , 2013 .

[19]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[20]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[21]  Stephen P. Boyd,et al.  Proximal Algorithms , 2013, Found. Trends Optim..

[22]  J. Toland,et al.  NONLINEAR SUPERPOSITION OPERATORS , 1992 .

[23]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[24]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[25]  T. Steihaug The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[26]  Armin Rund,et al.  A hybrid semismooth quasi-Newton method for nonsmooth optimal control with PDEs , 2020, Optimization and Engineering.

[27]  Konstantin Pieper,et al.  Finite element discretization and efficient numerical solution of elliptic and parabolic sparse control problems , 2015 .

[28]  A. Milzarek Numerical methods and second order theory for nonsmooth problems , 2016 .

[29]  Yongfeng Li,et al.  A Regularized Semi-Smooth Newton Method with Projection Steps for Composite Convex Programs , 2016, J. Sci. Comput..

[30]  Michael Ulbrich,et al.  Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces , 2011, MOS-SIAM Series on Optimization.

[31]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[32]  Stephen M. Robinson,et al.  Normal Maps Induced by Linear Transformations , 1992, Math. Oper. Res..

[33]  Stefan Ulbrich,et al.  Optimization with PDE Constraints , 2008, Mathematical modelling.

[34]  Karl Kunisch,et al.  Magnetic Resonance RF Pulse Design by Optimal Control With Physical Constraints , 2018, IEEE Transactions on Medical Imaging.

[35]  J. Moreau Proximité et dualité dans un espace hilbertien , 1965 .

[36]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[37]  Muhammad Aslam Noor,et al.  On general quasi-variational inequalities , 2012 .