Paper Info
Title
A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization.
Abstract
We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at points of nondifferentiability of the problem functions. We present a line search algorithm for situations when the objective and constraint functions are locally Lipschitz and continuously differentiable on open dense subsets of R-n. Our method is based on a sequential quadratic programming (SQP) algorithm that uses an l(1) penalty to regularize the constraints. A process of gradient sampling (GS) is employed to make the search direction computation effective in nonsmooth regions. We prove that our SQP-GS method is globally convergent to stationary points with probability one and illustrate its performance with a MATLAB implementation.
Year
DOI
Venue
2012
10.1137/090780201
SIAM JOURNAL ON OPTIMIZATION
Keywords
Field
DocType
nonconvex optimization,nonsmooth optimization,constrained optimization,sequential quadratic programming,gradient sampling,exact penalization
Mathematical optimization,Algorithm,Stationary point,Line search,Lipschitz continuity,Quadratic programming,Sequential quadratic programming,Smoothness,Optimization problem,Mathematics,Constrained optimization
Journal
Volume
Issue
ISSN
22
2
1052-6234
Citations 
PageRank 
References 
22
0.90
12
Authors
2
Name
Order
Citations
PageRank
Frank E. Curtis143225.71
Michael L. Overton2634590.15