Research

Research Interests

My current interests include:

• Nonlinear programming;

• Continuous optimization;

• Mixed-integer programming;

• Large-scale optimization methods for machine learning.

My long-term interests include:

• Convex analysis, networks, numerical analysis, numerical linear algebra;

• Algebra, computational algebraic geometry, cryptography, large-scale decomposition, game theory;

• Statistics.

Publications

• Efficient and Exact Polynomial-Time Solver for the Two Trust-Region Subproblem

  • Yibo Xu.

• Exact Matrix-Vector Multiplication Complexity for Kernel Projection and Its Application on Distributed Consensus Optimization

  • Yunheng Jiang, Yuyuan Ouyang, and Yibo Xu.

• Parallel and distributed asynchronous adaptive stochastic gradient methods

  • Yangyang Xu, Yibo Xu, Yonggui Yan, Colin Sutcher-Shepard, Leopold Grinberg, and Jie Chen.

  • Mathematical Programming Computation, Vol. 15, No. 3, pp. 471-508, 2023

• Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization

  • Yangyang Xu and Yibo Xu.

  • Journal of Optimization Theory and Applications, Vol. 196, No. 1, pp. 266-297, 2023

• Distributed stochastic inertial-accelerated methods with delayed derivatives for nonconvex problems

  • Yangyang Xu, Yibo Xu, Yonggui Yan, and Jie Chen.

  • SIAM Journal on Imaging Sciences, Vol. 15, No. 2, pp. 550-590, 2022.

• Katyusha Acceleration for Convex Finite-Sum Compositional Optimization

  • Yibo Xu and Yangyang Xu.

  • INFORMS Journal on Optimization, Vol. 3, No. 4, pp. 418-443, 2021.

• Convex Hull Derivation for a Symmetric Multilinear Polynomial and a Symmetric Polytope

  • Yibo Xu.

• Convex Hulls of Symmetric Multilinear Polynomials over Box Constraints

  • Yibo Xu, Warren Adams and Akshay Gupte.

• Error bounds for monomial convexification in polynomial optimization

  • Warren Adams, Akshay Gupte and Yibo Xu.

  • Mathematical Programming Series A, Vol. 175, No. 1, pp. 355-393, 2019.

• Other Solutions for the 2nd Problem in the Second Round of National Senior High School's Mathematical Competition of China in 2005 (in Chinese)

  • Yibo Xu.

  • High-School Mathematics, No. 8, pp. 19-21, 2007.

• Proof of a set of inequalities (in Chinese)

  • Yibo Xu and Shuineng Yu.

  • Bulletin of Mathematics, No. 18, pp. 46-47, 2004.

Former students

• Yuheng Jiang (Ph.D., Summer 2024)

  • Next position: quantitative analyst at Wells Fargo

• "Tina" Yidan Guo (Ph.D., Summer 2024)

  • Next position: lecturer at Zhejiang Shuren University