On the complexity of finding first-order critical points in constrained nonlinear optimization

Mathematical Programming

Volumn 144, Issue 1-2, 2014, Pages 93-106

  Cartis, Coralia ^a   Gould, Nicholas I M ^b   Toint, Philippe L ^c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^c University of Namur   (Belgium)

Author keywords

Constrained nonlinear optimization; Evaluation complexity; Worst case analysis

Indexed keywords

FUNCTION EVALUATION;

CONSTRAINED NON-LINEAR OPTIMIZATIONS; CONSTRAINED OPTIMI-ZATION PROBLEMS; EVALUATION COMPLEXITY; FIRST-ORDER; HOMOTOPY ALGORITHMS; OBJECTIVE FUNCTIONS; WORST-CASE ANALYSIS;

CONSTRAINED OPTIMIZATION;

EID: 84897112534     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-012-0617-9     Document Type: Article

References (15)

1. Byrd, R.H., Gould, N.I.M., Nocedal, J., Waltz, R.A.: On the convergence of successive linear-quadratic programming algorithms. SIAM J. Optim. 16(2), 471-489 (2005)
2. Cartis, C., Gould, N.I.M., Toint, Ph.L.: On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization. SIAM J. Optim. 20, 2833-2852 (2010)
3. Cartis, C., Gould, N.I.M., Toint, Ph.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results. Math. Program. Ser. A 127(2), 245-295 (2011)
4. Cartis, C., Gould, N.I.M., Toint, Ph.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- And derivative-evaluation complexity. Math. Program. Ser. A 130, 295-319 (2011)
5. Cartis, C., Gould, N.I.M., Toint, Ph.L.: On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. SIAM J. Optim. 21(4), 1721-1739 (2011)
6. Cartis, C., Gould, N.I.M., Toint, Ph.L.: Optimal Newton-type methods for nonconvex smooth optimization problems. ERGO technical report 11-009, School of Mathematics, University of Edinburgh (2011)
7. Cartis, C., Gould, N.I.M., Toint, Ph.L.: A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function. ERGO technical report 11-013, School of Mathematics, University of Edinburgh (2011)
8. Cartis, C., Gould, N.I.M., Toint, Ph.L.: On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization. SIAM J. Optim. 22(1), 66-86 (2012)
9. Cartis, C., Gould, N.I.M., Toint, Ph.L.: An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity. IMA J. Numer. Anal. 32(4), 1662-1695 (2012)
10. Gratton, S., Sartenaer, A., Toint, Ph.L.: Recursive trust-region methods for multiscale nonlinear optimization. SIAM J. Optim. 19(1), 414-444 (2008)
11. Nesterov, Y.: Introductory Lectures on Convex Optimization. Applied Optimization. Kluwer, Dordrecht (2004)
12. Nesterov, Y., Polyak, B.T.: Cubic regularization of Newton method and its global performance. Math. Program. Ser. A 108(1), 177-205 (2006)
13. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)
14. Vavasis, S.A.: Black-box complexity of local minimization. SIAM J. Optim. 3(1), 60-80 (1993)
15. Vicente, L.N.: Worst case complexity of direct search. Preprint 10-17, Department of Mathematics, University of Coimbra, Coimbra, Portugal, Euro J. Comput. Optim. (2010, to appear)