Locally Feasibly Projected Sequential Quadratic Programming for Nonlinear Programming on Arbitrary Smooth Constraint Manifolds

11/05/2021
by   Kevin S. Silmore, et al.
0

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(nm^2)-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.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

07/17/2021

On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems

We introduce a class of first-order methods for smooth constrained optim...
05/27/2022

Asymptotic Convergence Rate and Statistical Inference for Stochastic Sequential Quadratic Programming

We apply a stochastic sequential quadratic programming (StoSQP) algorith...
10/11/2019

Theory of functional connections applied to nonlinear programming under equality constraints

This paper introduces an efficient approach to solve quadratic programmi...
01/08/2021

Nonlinear Optimization in R using nlopt

In this article, we present a problem of nonlinear constraint optimizati...
06/18/2020

An Integer Linear Programming Framework for Mining Constraints from Data

Various structured output prediction problems (e.g., sequential tagging)...
05/09/2018

Robust-to-Dynamics Optimization

A robust-to-dynamics optimization (RDO) problem is an optimization probl...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.