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math.OC2023★ 1 cited
Differential-Equation Constrained Optimization With Stochasticity
Qin Li, Li Wang, Yunan Yang
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the mo…
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…