Xiaopeng Li Email & Phone Number

Key Achievements :-- Proposed a new concept "local minima at infinity" and new frameworks to study the landscape of noncoercive functions at infinity, and applied it to applications in machine learning, including artificial neural network and low rank matrix recovery.- Established global convergence of momentum method for smooth semialgebraic functions, relaxed two classical assumptions, globally Lipschitz gradient and coercivity, and improved the global convergence rate from O(1/√k) to o(1/k).- Implemented SGD and various types of momentum method on deep neural networks with different architectures using the same effective stepsize; the momentum method converged with a larger effective stepsize on 90% of experiments.- Presented and discussed state of art algorithms, analysis techniques and new research trends in an optimization study group with over 10 other researchers every month.

Golden, Colorado, United States

Proposed a novel variant of progressive hedging algorithm for solving multi-stage stochastic MILP and incorporated it in the mpi-sppy package, achieving better solutions within less iterations on 4 stochastic server location problems. Applied a new L1-penalized ADMM algorithm to solve transmission expansion problem and implemented it in both Python and Julia, achieving better solutions than intuitive solutions selected by humans.Collaborated with other two colleagues to test new algorithms over various instances on HPC and analyzed performance.

As a visiting Ph.D. student researcher at Shenzhen Research Institute of Big Data, I developed and maintained the interior point module in a large-scale linear programming solver with other 3 colleagues. I also assisted in performing end-to-end performance testing of the solver on the cluster sever. Key Achievements :-- Integrated a sparse direct linear solver into the interior point method module of a large-scale linear programming solver (HiGHS) and cut down the shifted geometric mean (SGM) ratio to Gurobi over Mittlemann's benchmark from 5.8 to 2.5. - Implemented cost perturbation strategy in the interior point method module to tackle the degeneracy issue of the reduced KKT system and cut down the SGM ratio from 2.5 to 2.3. - Designed a new dualizing strategy based on problem dimension and sparsity of the symbolic Cholesky factors to determine solving primal or dual problem and reduced the SGM ratio from 2.3 to 2.0. - Cooperated with 3 colleagues in other groups to simplify the crossover and clean up stages of the interior point method to obtain a vertex solution more efficiently and decreased the SGM ratio from 2.0 to 1.7.

As an undergraduate teaching assistant at the Chinese University of Hong Kong, Shenzhen, I taught recitations of mathematics courses to help younger students with course materials and homework questions, and held weekly office hours to answer additional questions from students. I also designed diagnostic test, collected feedback from students and helped them communicate with instructors more efficiently. Key Achievements :-- Instructed recitations of Elementary Real Analysis, Ordinary Differential Equations and Mathematical Analysis I & II with 100+ students for 3 years; customized teaching strategies for students with varied background. - Wrote and collected 200+ pages of lecture notes, recitation notes and practice questions with solutions for the instructors and students. - Collected suggestions for improving the course design and teaching quality for 4+ courses.

Doctor Of Philosophy - Phd, Operations Research

Activities and Societies: Teaching Assistant, Graduate Research Assistant, Member of Society for Industrial and Applied Mathematics

Bachelor Of Science - Bs, Applied Mathematics

Activities and Societies: Activities and Societies: Representative of Student Congress, Undergraduate Student Teaching Fellows.