Welcome to Pang Chin How, Jeffrey's webpage.


冯振豪 (My Chinese Name in Unicode)

email: matpchj@nus.edu.sg

I am an assistant professor in Mathematics at the National University of Singapore

My PhD Adviser is Adrian Lewis.
Recently, I am working on accelerating the method of alternating projection methods. I was also working on work on set-valued analysis and applying the theory to Differential Inclusions (which encompasses Optimal Control and the Calculus of Variations; More honestly, I worked on the discretized problem, and I hope to come back to that soon). Some of these topics fall under what is now known as Variational Analysis. In the past, I worked on semi-algebraic Variational Analysis, Numerical methods for the mountain pass, and Pseudospectra.


Papers (and slides):

Improved analysis of algorithms based on supporting halfspaces and quadratic programming for the convex intersection and feasibility problems (Slides)

SHDQP: An algorithm for convex set intersection problems based on supporting hyperplanes and dual quadratic programming (Slides)

Set Intersection Problems: Supporting hyperplanes and Quadratic Programming (Slides) (Accepted in 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, 2011.

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.


Other writings:

Finding saddle points of mountain pass type with quadratic models on affine spaces (code) (Slides)

First order dependence on uncertainty sets in robust optimization (Slides) (with thanks to Henry Wolkowicz)

Level set methods for finding critical points of general Morse index (Slides)

Research:

A recent research statement (3 pages, if you ignore 2 figures and references behind) and an older, more detailed statement

Education and employment:

September 2010 onwards: 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