Active set truncated-newton algorithm for simultaneous optimization of distillation column

Abstract

An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.

Keywords

simultaneous optimization of distillation column / active set truncated-Newton algorithm / modified augmented Lagrange multiplier methods / numerical experiment

References

[1] ChristofidesP D. Control of nonlinear distributed process systems: recent developments and challenges [J]. AICHE J, 2001, 47(2): 514-518

[2] BieglerL T, CervantesA, WaechterA. Advances in simultaneous strategies for dynamic process optimization[J]. Chemical Engineering Science, 2002, 57(3): 575-593

[3] VassiliadisV S, FloudasC A. The modified barrier function approach for large-scale optimization [J]. Computers Chem Engng, 1997, 21(8): 855-874

[4] LiangX M. Modified augmented lagrange multiplier methods for large-scale chemical process optimization [J]. Chinese J Chem Eng, 2001, 9(2): 167-172

[5] PytlakR. An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables[J]. SIAM J Optim, 1998, 8(2): 532-560

[6] ByrdR H, LuP, NocedalJ, et al.. A limited memory algorithm for bound constrained optimization [J]. SIAM J Sci Comput, 1995, 16(4): 1190-2108

[7] LiangX M, XuC X. A trust region algorithm for bound constrained minimization [J]. Optimization, 1997, 41(3): 279-289

[8] DemboR S, SteihaugT. Truncated-Newton algorithms for large-scale unconstrained optimization[J]. Math Prog, 1983, 26(2): 190-212

[9] NashS G, NocedalJ. A numerical study of the limited memory BFGS method and truncated-Newton method for large scale optimization [J]. SIAM J Optim, 1991, 1(2): 358-372

[10] NiQ, YuanY. A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization[J]. Math Comp, 1997, 66(220): 1509-1520

[11] SchittowskiKMore Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems[M], 1987, New York, Springer

[12] FacchineiF, JudiceJ, SoaresJ. An active set Newton algorithm for large-scale nonlinear programs with box constraints[J]. SIAM J Optim, 1998, 8(1): 158-186