- On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods Coralia Cartis(coralia.cartised.ac.uk) Nicholas I.M. Gould(nick.gouldstfc.ac.uk) Philippe L. Toint(philippe.tointunamur.be) Abstract: When solving the general smooth nonlinear optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy $\epsilon$ can be obtained by a second-order method using cubic regularization in at most $O(\epsilon^{-3/2})$ problem-functions evaluations, 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 least-squares. As a consequence, the presence of (possibly nonlinear) equality/inequality constraints does not affect the complexity of finding approximate first-order critical points in nonconvex optimization. This result improves on the best known ($O(\epsilon^{-2})$) evaluation-complexity bound for solving general nonconvexly constrained optimization problems. Keywords: Nonlinear optimization, evaluation complexity, general constrained problem Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares ) Category 3: Nonlinear Optimization (Bound-constrained Optimization ) Citation: @techreport{CartGoulToin13a, author={C. Cartis and N. I. M. Gould and Ph. L. Toint}, title = {On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods}, institution = {Namur Center for Complex Systems (NAXYS), University of Namur}, address = {Namur, Belgium}, number = {naXys-01-2013}, year = 2013} Download: [PDF]Entry Submitted: 04/03/2013Entry Accepted: 04/03/2013Entry Last Modified: 04/03/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.