On an inexact trust-region SQP-filter method for constrained nonlinear optimization

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• 作者：Andrea Walther ; Lorenz Biegler
• 关键词：Inexact trust region methods ; Filter approach ; General constrained nonlinear optimization
• 刊名：Computational Optimization and Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：63
• 期：3
• 页码：613-638
• 全文大小：618 KB
• 参考文献：1.Byrd, R.: Robust trust region methods for constrained optimization, Houston, USA. In: Third SIAM Conference on Optimization (1987)
  2.Byrd, R.H., Gilbert, J.C., Nocedal, J.: A trust region method based on interior point techniques for nonlinear programming. Math. Progr. 89, 149–185 (2000)CrossRef MathSciNet MATH
  3.Byrd, R.H., Curtis, F.E., Nocedal, J.: An inexact Newton method for nonconvex equality constrained optimization. Math. Progr. 122(2 (A)), 273–299 (2010)CrossRef MathSciNet MATH
  4.Conn, A.R., Gould, N.I., Toint, P.L.: LANCELOT: A Fortran Package for Large-scale Nonlinear Optimization (release A). Springer Series in Computational Mathematics, vol. 17. Springer Science & Business Media, New York (1992)MATH
  5.Conn, A.R., Gould, N.I., Toint, P.L.: Trust-Region Methods. SIAM, Philadelphia (2000)CrossRef MATH
  6.Conn, A.R., Scheinberg, K., Vicente, L.N.: Global convergence of general derivative-free trust-region algorithms to first- and second-order critical points. SIAM J. Opt. 20, 387–415 (2009)CrossRef MathSciNet MATH
  7.Curtis, F.E., Schenk, O., Wächter, A.: An interior-point algorithm for large-scale nonlinear optimization with inexact step computations. SIAM J. Sci. Comput. 32(6), 3447–3475 (2010)CrossRef MathSciNet MATH
  8.Fletcher, R., Gould, N., Leyffer, S., Toint, P., Wächter, A.: Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. SIAM J. Optim. 13(3), 635–659 (2002)CrossRef MathSciNet MATH
  9.Fletcher, R., Leyffer, S., Toint, P.: On the global convergence of a filter-SQP algorithm. SIAM J. Optim. 13(1), 44–59 (2002)CrossRef MathSciNet MATH
  10.Griewank, A., Walther, A.: Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation, 2nd edn. SIAM (2008)
  11.Griewank, A., Walther, A.: On constrained optimization by adjoint-based quasi-Newton methods. Optim. Methods Softw. 17, 869–889 (2002)CrossRef MathSciNet MATH
  12.Heinkenschloss, M., Ridzal, D.: A matrix-free trust-region sqp method for equality constrained optimization. Technical Report TR11-17, CAAM, Rice University (2011)
  13.Jiang, L., Biegler, L.T., Fox, G.: Optimization of pressure swing adsorption systems for air separation. AIChE J. 49, 1140–1157 (2003)CrossRef
  14.Omojokun, E.: Trust region algorithms for optimization with nonlinear equality and inequality constraints. PhD Thesis, Department of Computer Science, University of Colorado (1989)
  15.Vetukuri, S.R., Biegler, L.T., Walther, A.: An inexact trust-region algorithm for the optimization of periodic adsorption processes. Ind. Eng. Chem. Res. 49, 12004–12013 (2010)CrossRef
  16.Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Progr. 106(1), 25–57 (2006)CrossRef MATH
  17.Walther, A., Griewank, A.: Getting started with ADOL-C. In: Naumann, U., Schenk, O. (eds.) Combinatorial Scientific Computing, pp. 181–202. Chapman-Hall CRC Computational Science, London (2012)CrossRef
  18.Walther, A., Vetukuri, S.R.R., Biegler, L.T.: A first-order convergence analysis of trust-region methods with inexact Jacobians and inequality constraints. Optim. Methods Softw. 27(2), 373–389 (2012)CrossRef MathSciNet MATH
  19.Ziems, J.C., Ulbrich, S.: Adaptive multilevel inexact SQP methods for PDE-constrained optimization. SIAM J. Optim. 21(1), 1–40 (2011)CrossRef MathSciNet MATH
  
• 作者单位：Andrea Walther (1)
  Lorenz Biegler (2)
  
  1. Institut für Mathematik, Universität Paderborn, Paderborn, Germany
  2. Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operations Research and Mathematical Programming
  Operation Research and Decision Theory
  Statistics
  Convex and Discrete Geometry
  
• 出版者：Springer Netherlands
• ISSN：1573-2894

文摘

A class of trust-region algorithms is developed and analyzed for the solution of optimization problems with nonlinear equality and inequality constraints. These algorithms are developed for problem classes where the constraints are not available in an open, equation-based form, and constraint Jacobians are of high dimension and are expensive to calculate. Based on composite-step trust region methods and a filter approach, the resulting algorithms do not require the computation of exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices. With these modifications, we show that the algorithm is globally convergent. Also, as demonstrated on numerical examples, our algorithm avoids direct computation of exact Jacobians and has significant potential benefits on problems where Jacobian calculations are expensive.