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2017 | OriginalPaper | Chapter

13. A SQP Algorithm with Successive Error Restoration: NLPQLP

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Abstract

Let us consider the general nonlinear optimization problem with equality and inequality constraints:where it is assumed that the functions f :  n  → , and c i  :  n  → , i = 1 ,  …  , m, are twice continuously differentiable. Also, assume that

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Literature
go back to reference Armijo, L. (1966). Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics, 16(1), 1–3.MathSciNetCrossRefMATH Armijo, L. (1966). Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics, 16(1), 1–3.MathSciNetCrossRefMATH
go back to reference Bergman, L. (1988). Energy policy modeling: a survey of general equilibrium approaches. Journal of Policy Modeling, 10(3), 377–399.MathSciNetCrossRef Bergman, L. (1988). Energy policy modeling: a survey of general equilibrium approaches. Journal of Policy Modeling, 10(3), 377–399.MathSciNetCrossRef
go back to reference Bonnans, J. F., Panier, E. R., Tits, A. L., & Zhou, J. L. (1992). Avoiding the Maratos effect by means of a nonmonotone line search. II. Inequality constrained problems – feasible iterates. SIAM Journal on Numerical Analysis, 29, 1187–1202.MathSciNetCrossRefMATH Bonnans, J. F., Panier, E. R., Tits, A. L., & Zhou, J. L. (1992). Avoiding the Maratos effect by means of a nonmonotone line search. II. Inequality constrained problems – feasible iterates. SIAM Journal on Numerical Analysis, 29, 1187–1202.MathSciNetCrossRefMATH
go back to reference Deng, N. Y., Xiao, Y., & Zhou, F. J. (1993). Nonmonotonic trust-region algorithm. Journal of Optimization Theory and Applications, 26, 259–285.MathSciNetCrossRefMATH Deng, N. Y., Xiao, Y., & Zhou, F. J. (1993). Nonmonotonic trust-region algorithm. Journal of Optimization Theory and Applications, 26, 259–285.MathSciNetCrossRefMATH
go back to reference Grippo, L., Lampariello, F., & Lucidi, S. (1986). A nonmonotone line search technique for Newton’s method. SIAM Journal Numerical Analysis, 23, 707–716.MathSciNetCrossRefMATH Grippo, L., Lampariello, F., & Lucidi, S. (1986). A nonmonotone line search technique for Newton’s method. SIAM Journal Numerical Analysis, 23, 707–716.MathSciNetCrossRefMATH
go back to reference Grippo, L., Lampariello, F., & Lucidi, S. (1989). A truncated Newton method with nonmonotone line search for unconstrained optimization. Journal of Optimization Theory and Applications, 60, 401–419.MathSciNetCrossRefMATH Grippo, L., Lampariello, F., & Lucidi, S. (1989). A truncated Newton method with nonmonotone line search for unconstrained optimization. Journal of Optimization Theory and Applications, 60, 401–419.MathSciNetCrossRefMATH
go back to reference Grippo, L., Lampariello, F., & Lucidi, S. (1991). A class of nonmonotone stabilization methods in unconstrained optimization. Numerische Mathematik, 59, 779–805.MathSciNetCrossRefMATH Grippo, L., Lampariello, F., & Lucidi, S. (1991). A class of nonmonotone stabilization methods in unconstrained optimization. Numerische Mathematik, 59, 779–805.MathSciNetCrossRefMATH
go back to reference Liu, D. C., & Nocedal, J. (1989). On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45, 503–528.MathSciNetCrossRefMATH Liu, D. C., & Nocedal, J. (1989). On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45, 503–528.MathSciNetCrossRefMATH
go back to reference Manne, A. S. (1977). ETA-MACRO: A model of energy-economy interactions. In C. J. Hitch (Ed.), Modeling energy-economy interactions: Five approaches. Washington, DC, USA: Resources for the Future. Manne, A. S. (1977). ETA-MACRO: A model of energy-economy interactions. In C. J. Hitch (Ed.), Modeling energy-economy interactions: Five approaches. Washington, DC, USA: Resources for the Future.
go back to reference Murtagh, B. A., & Saunders, M. A. (1995). MINOS 5.4 user’s guide. (Technical Report SOL 83-20R, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California, CA 94305, February 1995). Murtagh, B. A., & Saunders, M. A. (1995). MINOS 5.4 user’s guide. (Technical Report SOL 83-20R, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California, CA 94305, February 1995).
go back to reference Panier, E. R., & Tits, A. L. (1991). Avoiding the Maratos effect by means of a nonmonotone line search. I: General constrained problems. SIAM Journal on Numerical Analysis, 28, 1183–1195.MathSciNetCrossRefMATH Panier, E. R., & Tits, A. L. (1991). Avoiding the Maratos effect by means of a nonmonotone line search. I: General constrained problems. SIAM Journal on Numerical Analysis, 28, 1183–1195.MathSciNetCrossRefMATH
go back to reference Powell, M. J. D. (1978b). The convergence of variable metric methods of nonlinearly constrained optimization calculations. In O. L. Mangasarian, R. R. Meyer, & S. M. Robinson (Eds.), Nonlinear programming 3 (pp. 27–63). New York, NY, USA: Academic.CrossRef Powell, M. J. D. (1978b). The convergence of variable metric methods of nonlinearly constrained optimization calculations. In O. L. Mangasarian, R. R. Meyer, & S. M. Robinson (Eds.), Nonlinear programming 3 (pp. 27–63). New York, NY, USA: Academic.CrossRef
go back to reference Raydan, M. (1993). On the Barzilai and Borwein choice of steplength for the gradient method. IMA Journal of Numerical Analysis, 13, 321–326.MathSciNetCrossRefMATH Raydan, M. (1993). On the Barzilai and Borwein choice of steplength for the gradient method. IMA Journal of Numerical Analysis, 13, 321–326.MathSciNetCrossRefMATH
go back to reference Raydan, M. (1997). The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM Journal on Optimization, 7, 26–33.MathSciNetCrossRefMATH Raydan, M. (1997). The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM Journal on Optimization, 7, 26–33.MathSciNetCrossRefMATH
go back to reference Schittkowski, K. (1983). On the convergence of a sequential quadratic programming method with an augmented Lagrange line search function. Mathematical Operations forschung und Statistik (Series Optimization), 14(2), 197–216.MathSciNetCrossRefMATH Schittkowski, K. (1983). On the convergence of a sequential quadratic programming method with an augmented Lagrange line search function. Mathematical Operations forschung und Statistik (Series Optimization), 14(2), 197–216.MathSciNetCrossRefMATH
go back to reference Schittkowski, K. (1985). NLPQL: A Fortran subroutine for solving constrained nonlinear programming problems. Annals of Operations Research, 5(2), 485–500.MathSciNetCrossRef Schittkowski, K. (1985). NLPQL: A Fortran subroutine for solving constrained nonlinear programming problems. Annals of Operations Research, 5(2), 485–500.MathSciNetCrossRef
go back to reference Schittkowski, K. (1986). NLPQL: A Fortran subroutine solving constrained nonlinear programming problems. Annals of Operations Research, 5, 485–500.MathSciNetCrossRef Schittkowski, K. (1986). NLPQL: A Fortran subroutine solving constrained nonlinear programming problems. Annals of Operations Research, 5, 485–500.MathSciNetCrossRef
go back to reference Schittkowski, K. (2002). NLPQLP: A Fortran implementation of a sequential quadratic programming algorithm. User’s guide. (Report, Department of Mathematics, University of Bayreuth). Schittkowski, K. (2002). NLPQLP: A Fortran implementation of a sequential quadratic programming algorithm. User’s guide. (Report, Department of Mathematics, University of Bayreuth).
go back to reference Schittkowski, K. (2005). QL: A Fortran code for convex quadratic programming. User’s guide, Version 2.11. (Technical report, Department of Mathematics, University of Bayreuth, July 2005). Schittkowski, K. (2005). QL: A Fortran code for convex quadratic programming. User’s guide, Version 2.11. (Technical report, Department of Mathematics, University of Bayreuth, July 2005).
go back to reference Schittkowski, K. (2009). NLPQO: A Fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search. User’s guide, version 3.0. (Technical Report, Department of Computer Science, University of Bayreuth). Schittkowski, K. (2009). NLPQO: A Fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search. User’s guide, version 3.0. (Technical Report, Department of Computer Science, University of Bayreuth).
go back to reference Schittkowski, K. (2010). A robust implementation of a sequential quadratic programming algorithm with successive error restoration. (Technical Report, Department of Computer Science, University of Bayreuth, 2010). Schittkowski, K. (2010). A robust implementation of a sequential quadratic programming algorithm with successive error restoration. (Technical Report, Department of Computer Science, University of Bayreuth, 2010).
go back to reference Toint, P. L. (1996). An assessment of nonmonotone line search techniques for unconstrained optimization. SIAM Journal on Scientific Computing, 17, 725–739.MathSciNetCrossRefMATH Toint, P. L. (1996). An assessment of nonmonotone line search techniques for unconstrained optimization. SIAM Journal on Scientific Computing, 17, 725–739.MathSciNetCrossRefMATH
go back to reference Toint, P. L. (1997). A nonmonotone trust-region algorithm for nonlinear optimization subject to convex constraints. Mathematical Programming, 77, 69–94.MathSciNetMATH Toint, P. L. (1997). A nonmonotone trust-region algorithm for nonlinear optimization subject to convex constraints. Mathematical Programming, 77, 69–94.MathSciNetMATH
Metadata
Title
A SQP Algorithm with Successive Error Restoration: NLPQLP
Author
Neculai Andrei
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-58356-3_13

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