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An infeasible nonmonotone SSLE algorithm for nonlinear programming

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Abstract

In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessary to choose a problematic penalty parameter. The new algorithm only needs to solve three systems of linear equations with the same nonsingular coefficient matrix. Under some suitable conditions, the global convergence is established. Some numerical results are also presented.

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References

  • Boggs PT, Tolle JW (1995) Sequential quadratic programming. Acta Numerica 1–51

  • Dolan ED, Moré J (2000) Benchmarking optimization software with Cops. Technical report MCS-TM-246, MCS Division, Argonne National Laboratory, Argonne

  • Fletcher R, Leyffer S (2002) Nonlinear programming without a penalty function. Math Program 91(2): 239–269

    Article  MATH  MathSciNet  Google Scholar 

  • Floudas CA (1995) Nonlinear and mixed-integer optimization. Topics in chemical engineering. Oxford University Press, New York

    Google Scholar 

  • Gao ZY, He GP, Wu F (1997a) Sequential systems of linear equations algorithm for nonlinear optimization problems with general constraints. J Optim Theory Appl 95(2): 371–397

    Article  MATH  MathSciNet  Google Scholar 

  • Gao ZY, He GP, Wu F (1997b) An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point. Sci China Ser A 40(6): 561–571

    Article  MATH  MathSciNet  Google Scholar 

  • Grossmann IE (2002) Review of nonlinear mixed-integer and disjunctive programming techniques. Optim Eng 3: 227–252

    Article  MATH  MathSciNet  Google Scholar 

  • Hager WW (1999) Stabilized sequential quadratic programming. Comput Optim Appl 12: 253–273

    Article  MATH  MathSciNet  Google Scholar 

  • Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes, vol 187, Lectures notes in economics and mathematical systems. Springer, Berlin

  • Jian JB, Lai YL, Zhang KC (2002) A feasible method for superlinearly and quadratically convergent sequential systems of equations. Acta Math Sin 45: 1137–1146 (in Chinese)

    MATH  MathSciNet  Google Scholar 

  • Li JL, Jian JB (2005) A superlinearly convergent SSLE algorithm for optimization problems with linear complementarity constraints. J Global Optim 33(4): 477–510

    Article  MATH  MathSciNet  Google Scholar 

  • Murtagh BA, Saunders MA (1982) A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints. Math Program Stud 16: 84–117

    MATH  MathSciNet  Google Scholar 

  • NEOS Server: http://www-neos.mcs.anl.gov/neos/solvers/nco:MINOS/AMPL.html

  • Panier ER, Tits AL, Herskovits JN (1988) A QP-free globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization. SIAM J Control Optim 26: 788–811

    Article  MATH  MathSciNet  Google Scholar 

  • Powell MJD (1978) A fast algorithm for nonlinearly constrained optimization calculations. In: Watson GA (ed) Numerical analysis, 1977, pp 144–157, Springer, Berlin

  • Qi HD, Qi LQ (2000) A new QP-free globally convergent, locally superlinear convergent algorithm for inequality constrained optimization. SIAM J Optim 11: 113–132

    Article  MATH  MathSciNet  Google Scholar 

  • Qi LQ, Yang YF (2002) A globally and superlinearly convergent QP-free algorithm for nonlinear constrained optimization. J Optim Theory Appl 113: 297–323

    Article  MATH  MathSciNet  Google Scholar 

  • Ulbrich M, Ulbrich S (2003) Nonmonotone trust-region methods for nonlinear equality constrained optimization without a penalty function. Math Program 95(1): 103–135

    Article  MATH  MathSciNet  Google Scholar 

  • Xu YF, Wang W (2001) A QP-free and superlinearly convergent algorithm for inequality constrained optimization. Acta Math Sci 21(1): 121–130

    MATH  MathSciNet  Google Scholar 

  • Yang YF, Li DH, Qi LQ (2003) A feasible sequential linear equation method for inequality constrained optimization. SIAM J Optim 13(4): 1222–1244

    Article  MATH  MathSciNet  Google Scholar 

  • Zhu ZB (2007) An interior point type QP-free algorithm with superlinear convergence for inequality constrained optimization. Appl Math Model 31: 1201–1212

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, 200092, Shanghai, China

    Chungen Shen & Dingguo Pu

  2. Department of Applied Mathematics, Shanghai Finance University, 201209, Shanghai, China

    Chungen Shen

  3. Department of Mathematics and Physics, Shanghai University of Electric Power, 200090, Shanghai, China

    Wenjuan Xue

Authors
  1. Chungen Shen
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  2. Wenjuan Xue
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  3. Dingguo Pu
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Corresponding author

Correspondence to Chungen Shen.

Additional information

This research is supported by National Science Foundation of China (No. 10771162); Talents Introduction Foundation (No. F08027); Innovation Program of Shanghai Municipal Education Commission (No. 09YZ408) and Shanghai Excellent Young Teacher Foundation (No. sdl08015).

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Shen, C., Xue, W. & Pu, D. An infeasible nonmonotone SSLE algorithm for nonlinear programming. Math Meth Oper Res 71, 103–124 (2010). https://doi.org/10.1007/s00186-009-0287-4

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  • DOI: https://doi.org/10.1007/s00186-009-0287-4

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