Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

Complexity analysis of interior point algorithms for non-Lipschitz and nonconvex minimization

(2014) Wei Bian et al.   MATHEMATICAL PROGRAMMING

On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization

(2014) Geovani N. Grapiglia et al.   MATHEMATICAL PROGRAMMING

An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity

(2012) C. Cartis et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Complexity bounds for second-order optimality in unconstrained optimization

(2011) C. Cartis et al.   JOURNAL OF COMPLEXITY

Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization

(2011) Coralia Cartis et al.   OPTIMIZATION METHODS & SOFTWARE

Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity

(2010) Coralia Cartis et al.   MATHEMATICAL PROGRAMMING

Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares

(2010) S. Bellavia et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems

(2010) C. Cartis et al.   SIAM JOURNAL ON OPTIMIZATION

Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results

(2009) Coralia Cartis et al.   MATHEMATICAL PROGRAMMING

Recursive Trust-Region Methods for Multiscale Nonlinear Optimization

(2008) Serge Gratton et al.   SIAM JOURNAL ON OPTIMIZATION