Rice University
Department of Computational and Applied Mathematics
6100 Main St., MS 134
Houston, Texas 77005-1892

Curriculum Vitae

• parametric nonlinear programming
• robust nonlinear programming
• chemical engineering applications
• computational image processing
• large-scale nonlinear programming
• other interests

• CAAM 335: Matrix Analysis
• Courses taught in previous semesters
• CAAM 210: Introduction to Engineering Computation
• CHE 253K: Applied Statistics (Univeristy of Texas)
• Statement of Teaching Philosophy
• MAA Presentations

One way to account for uncertainty in optimization problems is to calculate the solution as a function of some number of uncertain parameters. Methods to do this for linear programs, integer programs, quadratic programs and nonlinear programs with only one uncertain parameter (1-pNLP) are more or less mature. My work focuses on combining and extending aspects of 1-pNLP with multi-dimensional predictor-corrector (implicit manifold approximation) algorithms and singularity/bifurcation theory to develop an algorithm for pNLP with an arbitrary number of parameters. The current implementation of my algorithm is called POPAK.

• CAAM Graduate Seminar, November 16, 2005
• Dissertation Abstract, July 2005

Another approach to uncertainty is to require robustness, that is, that the solution is feasible for all relevant parameter values. For nonlinear programs such a requirement results in a semi-infinite program (an NLP with an infinite number of constraints).

• Hale, Elaine T. and Yin Zhang. Case Studies for a first-order robust nonlinear programming formulation. Journal of Optimization Theory and Applications, 134(1) 27-45, 2007.
• First-order robust real-time optimization. Presented at the AIChE 2006 Annual Meeting.

The chemical engineering community has often turned to the tools of mathematical programming in order to design, control and optimize chemical processes. Specific techniques that I have investigated or contributed to include nonlinear model predictive control, real-time optimization and robust process design. Example problems include CSTR's (steady-state, batch and semi-batch), a heat exchanger network, a reactor-separator system, and a gas blending process.

Recent results show that the number of measurements required to capture compressible signals lies between the number of significant components and the length of the signal. This is in contrast to traditional sampling theory, which requires at least n measurements, where n is the length of the signal. The additional cost of taking fewer measurements is that the original signal must be reconstructed if it is to be observed or analyzed. This field of research is called compressed sensing. Fixed-Point Continuation (FPC) is the algorithm I developed in collaboration with Yin Zhang and Wotao Yin.

When mathematical programs are very large, it may not be computationally feasible or expedient to require any matrix factorizations or linear system solves. Thus it is worthwhile to develop algorithms that do not require such complicated linear algebra, but instead rely on matrix-vector multiplications and other low-cost operations. My work in computational image processing falls under this category.

• Covergence rate of an interior point gradient method for the totally non-negative least squares problem, preliminary report. Presented at the 2007 Joint Mathematics Meetings.

I have a strong personal and professional interest in sustainability issues, especially carbon-free energy sources and energy conservation. If you see any possibilities for collaboration along these lines, please contact me.

• 2006: Mathematics as Motivation in an Introductory Programming Course
• 2007: Introducing Eigenvalues by way of the Resolvent