2021/11/04 by Kevin S. Silmore, Silmore, Kevin S., James W. Swan +1
Computer Science · Mathematics · Physics and Astronomy · #Adaptive optics and wavefront sensing #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2111.03236
openalex publication_date 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
High-dimensional nonlinear optimization problems subject to nonlinear constraints can appear in several contexts including constrained physical and dynamical systems, statistical estimation, and other numerical models. Feasible optimization routines can sometimes be valuable if the objective function is only defined on the feasible set or if numerical difficulties associated with merit functions or infeasible termination arise during the use of infeasible optimization routines. Drawing on the Riemannian optimization and sequential quadratic programming literature, a practical algorithm is constructed to conduct feasible optimization on arbitrary implicitly defined constraint manifolds. Specifically, with n (potentially bound-constrained) variables and m < n nonlinear constraints, each outer optimization loop iteration involves a single O(nm2)-flop factorization, and computationally efficient retractions are constructed that involve O(nm)-flop inner loop iterations. A package, LFPSQP.jl, is created using the Julia language that takes advantage of automatic differentiation and projected conjugate gradient methods for use in inexact/truncated Newton steps.