# zbMATH — the first resource for mathematics

A line search SQP method without a penalty or a filter. (English) Zbl 1317.90278
Summary: This paper describes a new algorithm for nonlinear programming problems with inequality constraints. The proposed approach first solves a sequence of quadratic programming subproblems via the line search technique and to induce the global convergence, it establishes a new step acceptance mechanism that is neither a penalty function nor a filter. A nonmonotone line search technique from the unconstraint optimization is applied to accelerate the algorithm. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical results are presented that show the potential efficiency of the new approach.

##### MSC:
 90C30 Nonlinear programming
##### Keywords:
nonlinear programming; line search; SQP; filter; global convergence
ipfilter; SNOPT
Full Text:
##### References:
 [1] Audet C, Dennis JE (2000) A pattern search filter method for nonlinear programming without derivatives. Department of Computational and Applied Mathematics, Rice University, Houston Technical Report · Zbl 1073.90066 [2] Benson HY, Shanno DF, Vanderbei RJ (2001) Interior-point methods for nonconvex nonlinear programming:filter methods and merit functions, Technical Report ORFE-00-06. Princeton University, Operations Research and Financial Engineering · Zbl 1259.90140 [3] Bielschowsky, RH; Gomes, FAM, Dynamic control of infeasibility in equality constrained optimization, SIAM J Optim, 19, 1299-1325, (2008) · Zbl 1178.65063 [4] Chin, CM; Fletcher, R, On the global convergence of an SLP-filter algorithm that takes EQP steps, Math Progr, 96, 161-177, (2003) · Zbl 1023.90060 [5] Chin, CM; Rashid, AA; Nor, KM, Global and local convergence of a filter line search method for nonlinear programming, Optim Method Softw, 22, 365-390, (2007) · Zbl 1193.90192 [6] Dolan, ED; Moré, JJ, Benchmarking optimization software with performance profiles, Math Progr, 91, 201-213, (2002) · Zbl 1049.90004 [7] Fletcher R, Gould NIM, Leyffer S, Toint PHL, W$$\ddot{a}$$chter A (2002) Global convergence of trust-SQP filter algorithms for general nonlinear programming. SIAM J Optim 13:635-659 · Zbl 1038.90076 [8] Fletcher, R; Leyffer, S, Nonlinear programming without a penalty function, Math Progr, 91, 239-270, (2002) · Zbl 1049.90088 [9] Fletcher R, Leyferr S (1999) A bundle filter method for nonsmooth nonlinear optimization, Numerical Analysis Report NA/195. Department of Mathematics, University of Dundee, Scotland · Zbl 1210.90176 [10] Fletcher, R; Leyffer, S; Toint, PhL, On the global convergence of a filter-SQP algorithm, SIAM J Optim, 13, 44-59, (2002) · Zbl 1029.65063 [11] Gill, PE; Murray, W; Saunders, MA, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM Rev, 47, 99-131, (2005) · Zbl 1210.90176 [12] Gonzaga, CC; Karas, EW; Vanti, M, A globally convergent filter method for nonlinear programming, SIAM J Optim, 14, 646-669, (2003) · Zbl 1079.90129 [13] Gould, NIM; Toint, PHL, Nonlinear programming without a penalty function or a filter, Math Progr, 122, 155-196, (2010) · Zbl 1216.90069 [14] Hock W, Schittkowski K (1981) Text examples for nonlinear programming codes, vol 187. Lecture Notes in Economics and Mathematics System. Springer, New York · Zbl 0452.90038 [15] Liu, XW; Yuan, YX, A sequential quadratic programming method without a penalty or a filter for nonlinear equality constrained optimization, SIAM J Optim, 21, 545-571, (2011) · Zbl 1233.90257 [16] Martínez, JM, Inexact restoration method with Lagriangian tangent decrease and new merit function for nonlinear programming, J Optim Theory Appl, 111, 39-58, (2001) · Zbl 1052.90089 [17] Shen, CG; Leyffer, S; Fletcher, R, A nonmonotone filter method for nonlinear optimization, Comput Optim Appl, 52, 583-607, (2012) · Zbl 1259.90140 [18] Powell, MJD; Watson, GA (ed.), A fast algorithm for nonlinearly constrained optimization calculations, 144-157, (1978), Berlin [19] Ulbrich, M; Ulbrich, S; Vicente, LN, A globally convergent primal-dual interior-point filter method for nonlinear programming, Math Progr, 100, 379-410, (2004) · Zbl 1070.90110 [20] Ulbrich, S, On the superlinear local convergence of a filter-SQP method, Math Progr, 100, 217-245, (2004) · Zbl 1146.90525 [21] Wächter, A; Biegler, LT, Line search filter methods for nonlinear programming, SIAM J Optim, 16, 1-31, (2005) · Zbl 1114.90128 [22] Yuan YX (1994) Trust region algorithms for nonlinear equations, Technical Report 049. Department of Mathematics, Hong Kong University, Hong Kong · Zbl 1114.90128 [23] Zhang, HC; Hager, WW, A nonmonotone line search technique and its application to unconstrained optimization, Soc Ind Appl Math, 14, 1043-1056, (2004) · Zbl 1073.90024
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.