Abstract
We employ the active set strategy which was proposed by Facchinei for solving large scale bound constrained optimization problems. As the special structure of the bound constrained problem, a simple rule is used for updating the multipliers. Numerical results show that the active set identification strategy is practical and efficient.
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References
J.V. Burke, J. J. Moré, G. Toraldo: Convergence properties of trust region methods for linear and convex constraints. Math. Program. 47 (1990), 305–336. zbl
L.F. Chen, Y. L. Wang, G. P. He: A feasible active set QP-free method for nonlinear programming. SIAM J. Optim. 17 (2006), 401–429. zbl
Z. Dostál: A proportioning based algorithm with rate of convergence for bound constrained quadratic programming. Numer. Algorithms 34 (2003), 293–302. zbl
F. Facchinei, A. Fischer, C. Kanzow: On the accurate identification of active constraints. SIAM J. Optim. 9 (1998), 14–32. zbl
F. Facchinei, J. Júdice, J. Soares: An active set Newton algorithm for large-scale nonlinear programs with box constraints. SIAM J. Optim. 8 (1998), 158–186. zbl
F. Facchinei, J. Júdice, J. Soares: Generating box-constrained optimization problems. ACM Trans. Math. Softw. 23 (1997), 443–447. zbl
F. Facchinei, S. Lucidi: Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems. J. Optimization Theory Appl. 85 (1995), 265–289. zbl
F. Facchinei, S. Lucidi, L. Palagi: A truncated Newton algorithm for large scale box constrained optimization. SIAM J. Optim. 12 (2002), 1100–1125. zbl
D.C. Liu, J. Nocedal: On the limited memory BFGS method for large scale optimization. Math. Program. 45 (1989), 503–528. zbl
J. J. Moré, G. Toraldo: On the solution of large quadratic programming problems with bound constraints. SIAM J. Optim. 1 (1991), 93–113. zbl
Q. Ni, Y. Yuan: A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization. Math. Comput. 66 (1997), 1509–1520. zbl
G. Di Pillo, F. Facchinei, L. Grippo: An RQP algorithm using a differentiable exact penalty function for inequality constrained problems. Math. Program. 55 (1992), 49–68. zbl
K. Schittkowski: More test examples for nonlinear programming codes. Lecture Notes in Economics and Mathematical Systems, Vol. 282. Springer, Berlin, 1987.
L. Sun, G. P. He, Y. L. Wang, L. Fang: An active set quasi-Newton method with projected search for bound constrained minimization. Comput. Math. Appl. 58 (2009), 161–170.
L. Sun, G. P. He, Y. L. Wang, C.Y. Zhou: An accurate active set Newton method for large scale bound constrained optimization. Appl. Math. Accepted.
Y. L. Wang, L.F. Chen, G. P. He: Sequential systems of linear equations method for general constrained optimization without strict complementarity. J. Comput. Appl. Math. 182 (2005), 447–471.
Y.H. Xiao, Z.X. Wei: A new subspace limited memory BFGS algorithm for large-scale bound constrained optimization. Appl. Math. Comput. 185 (2007), 350–359. zbl
C.Y. Zhou, G. P. He, Y. L. Wang: A new constraints identification technique-based QP-free algorithm for the solution of inequality constrained minimization problems. J. Comput. Math. 24 (2006), 591–608.
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The work was supported in part by the National Science Foundation of China (10571109, 10901094), Natural Science Foundation of Shandong (Y2008A01) and Technique Foundation of STA (2006GG3210009).
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Sun, L., Fang, L. & He, G. An active set strategy based on the multiplier function or the gradient. Appl Math 55, 291–304 (2010). https://doi.org/10.1007/s10492-010-0022-8
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DOI: https://doi.org/10.1007/s10492-010-0022-8