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math.OC2026
Convergence of a Randomized Newton Method in Nonconvex Optimization
Edward Huynh, Björn Engquist
We analyze a stochastic Newton optimization scheme for locating the unique global minimizer of a general nonconvex objective function. The method couples a Newton algorithm to addi…
math.OC2023
Adaptive State-Dependent Diffusion for Derivative-Free Optimization
Björn Engquist, Kui Ren, Yunan Yang
This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probabil…
math.OC2022
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization
Björn Engquist, Kui Ren, Yunan Yang
We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is th…