References
- C. Audet and J.E. Dennis Jr, Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim. 17 (2006), pp. 188–217. doi: 10.1137/040603371
- A.S. Bandeira, K. Scheinberg and L.N. Vicente, Convergence of trust-region methods based on probabilistic models, SIAM J. Optim. 24 (2014), pp. 1238–1264. doi: 10.1137/130915984
- A. Buckley, An alternative implementation of Goldfarb's minimization algorithm, Math. Program. 8 (1975), pp. 207–231. doi: 10.1007/BF01580443
- T.F. Coleman and Y. Li, A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints, Math. Program. 88 (2000), pp. 1–31. doi: 10.1007/PL00011369
- A.R. Conn, N.I.M. Gould and P.L. Toint, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM J. Numer. Anal. 25 (1988), pp. 433–460. doi: 10.1137/0725029
- A.R. Conn, K. Scheinberg and L.N. Vicente, Geometry of interpolation sets in derivative free optimization, Math. Program. 111 (2008), pp. 141–172. doi: 10.1007/s10107-006-0073-5
- A.R. Conn, K. Scheinberg and L.N. Vicente, Geometry of sample sets in derivative free optimization: Polynomial regression and underdetermined interpolation, IMA J. Numer. Anal. 28 (2008), pp. 721–748. doi: 10.1093/imanum/drn046
- A.R. Conn, K. Scheinberg and L.N. Vicente, Introduction to Derivative-Free Optimization, MPS-SIAM Series on Optimization, SIAM, Philadelphia, 2009.
- E.D. Dolan and J.J. More, Benchmarking optimization software with performance profiles, Math. Profiles 91 (2002), pp. 201–213.
- R. Durrett, Probability: Theory and Examples, 4th ed., Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 2010.
- A. Forsgren and W. Murray, Newton methods for large-scale linear inequality-constrained minimization, SIAM J. Optim. 7 (1997), pp. 162–176. doi: 10.1137/S1052623494279122
- D.M. Gay, A trust-region approach to linearly constrained optimization, in Numerical Analysis, D.F. Griffiths, ed., Lecture Notes in Mathematics, vol. 1066, Springer-Verlag, Berlin, Heidelberg, New York, 1984, pp. 72–105.
- P.E. Gill and W. Murray, Newton-type methods for unconstrained and linearly constrained optimization, Math. Program. 7 (1974), pp. 311–350. doi: 10.1007/BF01585529
- L. Grippo, F. Lampariello and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal. 23 (1986), pp. 707–716. doi: 10.1137/0723046
- W. Hock and K. Schittkowski, Test examples for nonlinear programming codes, Vol. 187 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1981.
- C. Kanzow and A. Klug, On affine scaling interior point Newton methods for nonlinear minimization with bound constraints, Preprint 255, Institute of Applied Mathematics and Statistics, University of Würzburg, September 2004.
- B.A. Murtagh and M.A. Saunders, Large-scale linearly constrained optimization, Math. Program. 14 (1978), pp. 41–72. doi: 10.1007/BF01588950
- M.J.D. Powell, On trust region methods for unconstrained minimization without derivatives, Math. Program. 97 (2003), pp. 605–623. doi: 10.1007/s10107-003-0430-6
- M.J.D. Powell, The BOBYQA algorithm for bound constrained optimization without derivatives. Cambridge NA Report NA2009/06, Cambridge: University of Cambridge, 2009.
- Yu. Nesterov, Efficiency of coordinate descent methods on huge-scale optimization problems, SIAM J. Optim. 22 (2012), pp. 341–362. doi: 10.1137/100802001
- K. Ritter, A superlinearly convergent method for minimization problems with linear inequality constraints, Math. Program. 4 (1973), pp. 44–71. doi: 10.1007/BF01584646
- K. Ritter, A method of conjugate directions for linearly constrained nonlinear programming problems, SIAM J. Numer. Anal. 12 (1975), pp. 273–303. doi: 10.1137/0712024
- K. Schittkowski, More test examples for nonlinear programming codes, Vol. 282 in Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1987.
- L.N. Vicente and A.L. Custódio, Analysis of direct searches for discontinuous functions, Math. Program. 133 (2012), pp. 299–325. doi: 10.1007/s10107-010-0429-8
- P. Wang and D. Zhu, An affine scaling derivative-free trust-region method for solving nonlinear systems subject to linear inequality constraints, Int. J. Comput. Math. 8 (2015), pp. 1660–1687. doi: 10.1080/00207160.2014.959942
- P. Wang and D. Zhu, A derivative-free affine scaling trust-region method with interior backtracking technique for bound-constrained nonlinear systems, J. Syst. Sci. Math. 37 (2015), pp. 155–171.
- E.K. Yang and D.J..W. Tolle, A class of methods for solving large, convex quadratic programs subject to box constraints, Math. Program. 51 (1991), pp. 223–228. doi: 10.1007/BF01586934
- H. Zhang and W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14 (2004), pp. 1043–1056. doi: 10.1137/S1052623403428208
- H. Zhang, A.R. Conn and K. Scheinberg, A derivative-free algorithm for least-squares minimization, SIAM J. Optim. 20 (2010), pp. 3555–3576. doi: 10.1137/09075531X
- D. Zhu, A new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints, J. Comput. Appl. Math. 161 (2003), pp. 1–25. doi: 10.1016/S0377-0427(03)00458-8
- D. Zhu, Superlinear convergence of affine scaling interior point newton method for linear inequality constrained minimization without strict complementarity, Acta Math. Appl. Sin. 25 (2009), pp. 183–194. doi: 10.1007/s10255-007-7029-2