3 papers
math.OC2025
A novel numerical method tailored for unconstrained optimization problems
Lin Li, Pengcheng Xie, Li Zhang
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical met…
math.NA2025
An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains
Yangyi Ye, Lin Li, Pengcheng Xie +1
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative prop…
math.OC2025
A spectral Levenberg-Marquardt-Deflation method for multiple solutions of semilinear elliptic systems
Lin Li, Yuheng Zhou, Pengcheng Xie +1
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to…