An infeasible QP-free algorithm without a penalty function or a filter for nonlinear inequality-constrained optimization

References

• AMPL, 2012. Available at http://www.ampl.com/BOOK/student_ed.html.
   Google Scholar
• P.T. Boggs and J.W. Tolle, Sequential Quadratic Programming, in Acta No., Vol. 4, Cambridge University Press, Cambridge, 1995, pp. 1–51.
   Google Scholar
• I. Bongartz, A.R. Conn, N.I. Gould, and PH.L. Toint, CUTE: Constrained and unconstrained testing environment, ACM Trans. Math. Softw. 21 (1995), pp. 123–160. doi: 10.1145/200979.201043
   Web of Science ®Google Scholar
• L.F. Chen, Y.L. Wang, and G.P. He, A feasible active set QP-free method for nonlinear programming, SIAM J. Optim. 17 (2006), pp. 401–429. doi: 10.1137/040605904
   Web of Science ®Google Scholar
• A.R. Conn, N.I.M. Gould, and Ph.L. Toint, Trust-Region Methods, SIAM, Philadelphia, PA, 2000.
   Google Scholar
• E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201–213. doi: 10.1007/s101070100263
   Web of Science ®Google Scholar
• F. Facchinei, A. Fischer, and C. Kanzow, On the accurate identification of active constraints, SIAM J. Optim. 9 (1998), pp. 14–32. doi: 10.1137/S1052623496305882
   Web of Science ®Google Scholar
• F. Facchinei and S. Lucidi, Quadratically and superlinearly convergent algorithm for large scale box constrained optimization, SIAM J. Optim. 12 (2002), pp. 265–289. doi: 10.1137/S1052623499359890
   Web of Science ®Google Scholar
• A. Forsgren, Inertia-controlling factorizations for optimization algorithms, Appl. Numer. Math. 43 (2002), pp. 91–107. doi: 10.1016/S0168-9274(02)00119-8
   Web of Science ®Google Scholar
• P.E. Gill, W. Murray, and M.A. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM Rev. 47 (2005), pp. 99–131. doi: 10.1137/S0036144504446096
   Web of Science ®Google Scholar
• W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes, in Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer-Verlag, Berlin Heidelberg New York, 1981. doi: 10.1007/978-3-642-48320-2
   Google Scholar
• J.B. Jian, R. Quan, and W.X. Cheng, A feasible QP-free algorithm combining the interior-point method with active set for constrained optimization, Comput. Math. Appl. 58 (2009), pp. 1520–1533. doi: 10.1016/j.camwa.2009.07.018
   Web of Science ®Google Scholar
• C. Kanzow and H.D. Qi, A QP-free constrained Newton-type method for variational inequality problems, Math. Program. 85 (1999), pp. 788–811.
   Web of Science ®Google Scholar
• X.W. Liu and Y.X. Yuan, A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization, SIAM J. Optim. 21 (2011), pp. 545–571. doi: 10.1137/080739884
   Web of Science ®Google Scholar
• J. Nocedal and S. Wright, Numerical Optimization, Springer-Verlag, New York, Inc., 1999.
   Google Scholar
• E.R. Panier, A.L. Tits, and J.N. Herskovits, A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J. Control Optim. 26 (1988), pp. 788–811. doi: 10.1137/0326046
   Web of Science ®Google Scholar
• M.J.J. Powell, The convergence of variable metric methods for nonlinearly constrained optimization calculations, in Nonlinear Programming, R.R. Meyer and S.M. Robinson, eds., Vol. 3, Academic Press, New York, 1978.
   Google Scholar
• H.D. Qi and L. Qi, A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J. Optim. 11 (2000), pp. 113–132. doi: 10.1137/S1052623499353935
   Web of Science ®Google Scholar
• L. Qi and Y.F. Yang, Globally and superlinearly convergent QP-free algorithm for nonlinear constrained optimization, J. Optim. Theory Appl. 113 (2002), pp. 297–323. doi: 10.1023/A:1014882909302
   Web of Science ®Google Scholar
• S.M. Robinson, Strongly regular generalized equations, Math. Oper. Res. 5 (1980), pp. 43–62. doi: 10.1287/moor.5.1.43
   Web of Science ®Google Scholar
• C. Shen, W. Xue, and X.D. Chen, Global convergence of a robust fiter SQP algorithm, Eur. J. Oper. Res. 206 (2010), pp. 34–45. doi: 10.1016/j.ejor.2010.02.031
   Web of Science ®Google Scholar
• A.L. Tits, A. Wächter, S. Bakhtiari, T.J. Urban, and C.T. Lawrence, A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties, SIAM J. Optim. 14 (2003), pp. 173–199. doi: 10.1137/S1052623401392123
   Web of Science ®Google Scholar
• R.J. Vanderbei and D.F. Shanno, An interior-point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl. 13 (1999), pp. 231–252. doi: 10.1023/A:1008677427361
   Web of Science ®Google Scholar
• Y.L. Wang, L.F. Chen, and G.P. He, Sequential systems of linear equations method for general constrained optimization without strict complementarity, J. Comput. Appl. Math. 182 (2005), pp. 447–471. doi: 10.1016/j.cam.2004.12.023
   Web of Science ®Google Scholar