冯振豪 (My Chinese Name in Unicode)
I am an assistant professor in Mathematics at the National University of Singapore
My PhD Adviser is Adrian Lewis.
My current research interest is the design of algorithms for distributed optimization mainly derived from Dykstra's algorithm (or block coordinate optimization on the dual) and problems involving alternating projections. I used to work on set-valued analysis (a part of variational analysis), spending some time extending the relationship between metric regularity, the Aubin property and linear openness, which I then applied to study Differential Inclusions (which encompasses Optimal Control and the Calculus of Variations; More honestly, I worked on the discretized problem). In the past, I worked on semi-algebraic Variational Analysis, Numerical methods for the mountain pass, and Pseudospectra.
Distributed deterministic asynchronous algorithms in time-varying graphs through Dykstra splitting (In third review, SIAM Journal on Optimization.)
Set Intersection Problems: Supporting hyperplanes and Quadratic Programming (Slides) February 2015, Volume 149, Issue 1–2, pp 329–359, (2015) Mathematical Programming
Subdifferential analysis of differential inclusions via discretization (Slides), Volume 253, Issue 1, 1 July 2012, Pages 203--224 (2012), Journal of Differential Equations
Characterizing generalized derivatives of set-valued maps: Extending the Tangential and Normal Approaches (Slides), (2013) SIAM J. Control Optim., 51(1), 145--171.
Implicit multifunction theorems with positively homogeneous maps Nonlinear Analysis: Theory, Methods and Applications, 75:1348–1361, 2012. (Special issue in variational analysis, edited by Boris Mordukhovich)
Generalized differentiation with
positively homogeneous maps: Applications to set-valued analysis and metric
regularity (Slides) Math. Oper. Res., 36:3:377–397,
Level set methods for finding critical points of mountain pass type(with Adrian S. Lewis) (Slides) (Nonlinear Analysis: Theory, Methods and Applications, 74:12, pp. 4058-4082 (2011))
Continuity and differentiability of set-valued maps revisited in the light of tame geometry(with Aris Daniilidis) (Slides) (Journal of the London Mathematical Society, 83:3, pp. 637-658 (2011))
Lipschitz behavior of the robust regularization(with Adrian S. Lewis), (SIAM Journal on Control and Optimization. Volume 8, No. 45, pp. 3080-3104 (2009)) (Slides)
Variational Analysis of Pseudospectra (with Adrian S. Lewis)(SIAM Journal on Optimization, Volume 19, Issue 3, pp. 1048-1072 (2008)) (Slides) (Poster)
Some principles for mountain pass algorithms, and the parallel distance.
First order dependence on uncertainty sets in robust optimization (Slides) (with thanks to Henry Wolkowicz)
Education and employment:
September 2010 - June 2012: Applied Math Instructor, MIT
July 2009- July 2010 Fields Institute and the University of Waterloo
Postdoctoral Fellow in Combinatorics and Optimization
August 2004- August 2009 Cornell University
PhD in Applied Mathematics
(I was at the CRM (Centre de Recerca Matemàtica) , UAB (Universitat Autònoma de Barcelona) working with Aris Daniilidis from 11 Sept 2008 to 8 December 2008.)
July 2003- July 2004 Singapore MIT Alliance
S.M in HPCES (High Performance Computation for Engineered Systems)
July 2000- July 2003 National University of Singapore (NUS)
Bsc in Mathematics, Computational Science