17 citations · 27 across the 7 of their papers we have counts for
8 papers
An adaptive regularization algorithm for unconstrained optimization with inexact function and derivatives values
N. I. M. Gould, Ph. L. Toint
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of…
Strong Evaluation Complexity Bounds for Arbitrary-Order Optimization of Nonconvex Nonsmooth Composite Functions
Coralia Cartis, Nick Gould, Philippe L. Toint
We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and…
Universal regularization methods - varying the power, the smoothness and the accuracy
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst secon…
Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints
Coralia Cartis, Nick I. M. Gould, Philippe L. Toint
We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enfor…
Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
Coralia Cartis, Nick I. M. Gould, Philippe L. Toint
We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving…
Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
The unconstrained minimization of a sufficiently smooth objective function is considered, for which derivatives up to order , , are assumed to be available. An a…
Evaluation complexity bounds for smooth constrained nonlinear optimisation using scaled KKT conditions, high-order models and the criticality measure
Coralia Cartis, Nick Gould, Philippe L Toint
Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of proved by Cartis, Gould and Toint (IMAJNA…
Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization
C. Cartis, N. I. M. Gould, Ph. L. Toint
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm…