zbMATH — the first resource for mathematics

An infeasible QP-free method without a penalty function for nonlinear inequality constrained optimization. (English) Zbl 1342.90187
Summary: In this paper, we present a new QP-free method without using a penalty function for inequality constrained optimization. It is an infeasible method. At each iteration, three linear equations with the same coefficient matrix are solved. The nearly active set technique is used in the algorithm, which eliminates some inactive constraints and reduces the dimension of coefficient matrix, and thereby reduces the amount of computational work. Moreover, the algorithm reduces the value of objective function or the measure of constraints violation according to the relationship between optimality and feasibility. Under common conditions, we prove that the proposed method has global and superlinear local convergence. Lastly, preliminary numerical results are reported.

90C30 Nonlinear programming
ipfilter; SNOPT
Full Text: DOI
[1] Boggs PT, Tolle JW (1995) Sequential quadratic programming. In: Acta No., vol 4. Cambridge University Press, Cambridge, pp 1-51 · Zbl 1188.90191
[2] Gill, PE; Murray, W; Saunders, MA, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM Rev, 47, 99-131, (2005) · Zbl 1210.90176
[3] Panier, ER; Tits, AL; Herskovits, JN, A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J Control Optim, 26, 788-811, (1988) · Zbl 0651.90072
[4] Qi, HD; Qi, L, A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J Optim, 11, 113-132, (2000) · Zbl 0999.90038
[5] Qi, L; Yang, YF, Globally and superlinearly convergent QP-free algorithm for nonlinear constrained optimization, J Optim Theory Appl, 113, 297-323, (2002) · Zbl 1027.90089
[6] Qiu, SQ; Chen, ZW, Global and local convergence of a class of penalty-free-type methods for nonlinear programming, Appl Math Model, 36, 3201-3216, (2012) · Zbl 1252.90078
[7] Facchinei, F; Fischer, A; Kanzow, C, On the accurate identification of active constraints, SIAM J Optim, 9, 14-32, (1998) · Zbl 0960.90080
[8] Fletcher, R; Leyffer, S, Nonlinear programming without a penalty function, Math Prog Ser A, 91, 239-269, (2002) · Zbl 1049.90088
[9] Ulbrich, M; Ulbrich, S; Vicent, N, A globally convergent primal-dual interior-point filter method for nonlinear programming, Math Prog, 100, 379-410, (2004) · Zbl 1070.90110
[10] Chin, CM; Rashid, AHA; Nor, KM, Global and local convergence of a filter line search method for nonlinear programming, Optim Meth Soft, 3, 365-390, (2007) · Zbl 1193.90192
[11] Shen, C; Xue, W; Chen, XD, Global convergence of a robust filter SQP algorithm, Eur J Oper Res, 206, 34-45, (2010) · Zbl 1188.90191
[12] Bueno, LF; Friedlander, A; Martínez, JM; Sobral, FNC, Inexact restoration method for derivative-free optimization with smooth constraints, SIAM J Optim, 23, 1189-1213, (2013) · Zbl 1280.65050
[13] Chen, LF; Wang, YL; He, GP, A feasible active set QP-free method for nonlinear programming, SIAM J Optim, 17, 401-429, (2006) · Zbl 1165.90640
[14] Fletcher, R; Leyffer, S, Nonlinear programming without a penalty function, Math Prog, 91, 239-269, (2002) · Zbl 1049.90088
[15] Yamashita H, Yabe H (2003) A globally convergent trust-region SQP method without a penalty function for nonlinearly constrained optimization. Technical report, Mathematical Systems Inc, Sinjuku-ku, Tokyo, Japan · Zbl 1070.90110
[16] Conn AR, Gould NIM, Toint PhL (2000) Trust-region methods. SIAM, Philadelphia · Zbl 0958.65071
[17] Nocedal J, Wright S (1999) Numerical optimization. Springer, New York · Zbl 0930.65067
[18] Kanzow, C; Qi, HD, A QP-free constrained Newton-type method for variational inequality problems, Math Pro, 85, 788-811, (1999)
[19] Robinson, SM, Strongly regular generalized equations, Math Oper Res, 5, 43-62, (1980) · Zbl 0437.90094
[20] Facchinei, F; Lucidi, S, Quadratically and superlinearly convergent algorithm for large scale box constrained optimization, SIAM J Optim, 12, 265-289, (2002) · Zbl 1035.90103
[21] Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes, vol 187. Lecture notes in economics and mathematical systems. Springer, Berlin · Zbl 0452.90038
[22] Powell, MJJ; Meyer, RR (ed.); Robinson, SM (ed.), The convergence of variable metric methods for nonlinearly constrained optimization calculations, No. 3, (1978), New York
[23] Wang, YL; Chen, LF; He, GP, Sequential systems of linear equations method for general constrained optimization without strict complementarity, J Comput Appl Math, 182, 447-471, (2005) · Zbl 1078.65055
[24] Dolan, ED; Moré, JJ, Benchmarking optimization software with performance profiles, Math Program, 91, 201-213, (2002) · Zbl 1049.90004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.