Projects per year
Abstract
When solving the general smooth nonlinear and possibly nonconvex optimization problem involving equality and/or inequality constraints, an approximate firstorder critical point of accuracy ∈ can be obtained by a secondorder method using cubic regularization in at most O(∈<sup>3/2</sup> ) evaluations of problem functions, the same order bound as in the unconstrained case. This result is obtained by first showing that the same result holds for inequality constrained nonlinear leastsquares. As a consequence, the presence of (possibly nonconvex) equality/inequality constraints does not affect the complexity of finding approximate firstorder critical points in nonconvex optimization. This result improves on the best known (O(∈<sup>2</sup> )) evaluationcomplexity bound for solving general nonconvexly constrained optimization problems.
Original language  English 

Pages (fromto)  836851 
Number of pages  16 
Journal  SIAM Journal on Numerical Analysis 
Volume  53 
Issue number  2 
DOIs  
Publication status  Published  2015 
Keywords
 Complexity theory
 Nonlinear optimization
 Constrained problems
 Leastsquares problems
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Projects
 2 Active

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research

Activities

A path and some adventures in the jungle of highorder nonlinear optimization
Philippe Toint (Speaker)
24 Oct 2017Activity: Talk or presentation types › Invited talk

How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Invited speaker)
5 Feb 2016Activity: Talk or presentation types › Oral presentation

Polytechnic University of Hong Kong
Philippe Toint (Visiting researcher)
31 Jan 2016 → 14 Feb 2016Activity: Visiting an external institution types › Research/Teaching in a external institution