Phương pháp lọc Lagrange mở rộng

Abhishek K, Leyffer S, Linderoth JT (2010) FilMINT: an outer-approximation-based solver for nonlinear mixed integer programs. INFORMS J Comput 22:555–567 Altay-Salih A, Pinar MC, Leyffer S (2003) Constrained nonlinear programming for volatility estimation with GARCH models. SIAM Rev 45(3):485–503 Arrieta-Camacho JJ, Biegler LT, Subramanian D (2007) NMPC-based real-time coordination of multiple aircraft. In: Allgower RF, Biegler LT (eds) Assessment and future directions of nonlinear model predictive control. Springer, Heidelberg, pp 629–639 Bautista G, Anjos MF, Vannelli A (2007) Formulation of oligopolistic competition in AC power networks: an NLP approach. IEEE Trans Power Syst 22(1):105–115 Belotti P, Kirches C, Leyffer S, Linderoth J, Luedtke J, Mahajan A (2013) Mixed-integer nonlinear optimization. Acta Numer 22(5):1–131 Benson H, Shanno D (2007) An exact primal-dual penalty method approach to warmstarting interior-point methods for linear programming. Comput Optim Appl 38:371–399. https://doi.org/10.1007/s10589-007-9048-6 Benson HY, Shanno DF (2008) Interior-point methods for nonconvex nonlinear programming: regularization and warmstarts. Comput Optim Appl 40(2):143–189 Benson HY, Shanno DF, Vanderbei RJ (2002) Interior-point methods for nonconvex nonlinear programming: filter-methods and merit functions. Comput Optim Appl 23(2):257–272 Bertsekas DP (1982) Constrained optimization and lagrange multiplier methods. Athena Scientific, New York Betts JT (2001) Practical methods for optimal control using nonlinear programming. Advances in design and control. SIAM, Philadelphia Biegler LT, Grossmann IE (2004a) Challenges and research issues for product and process design optimization. In: Floudas CA, Agrawal R (eds) Proceedings of foundations of computer aided process design. CACHE Corporation, Austin Biegler LT, Grossmann IE (2004b) Part I: retrospective on optimization. Comput Chem Eng 28(8):1169–1192 Birgin EG, Martinez JM (2008) Improving ultimate convergence of an augmented Lagrangian method. Optim Methods Softw 23(2):177–195 Birgin EG, Martínez JM (2012) Augmented lagrangian method with nonmonotone penalty parameters for constrained optimization. Comput Optim Appl 51(3):941–965 Birgin EG, Martínez JM (2014) Practical augmented Lagrangian methods for constrained optimization, vol 10. SIAM, Philadelphia Bonami P, Biegler LT, Conn AR, Cornuejols G, Grossmann IE, Laird CD, Lee J, Lodi A, Margot F, Sawaya N, Wähter A (2005) An algorithmic framework for convex mixed integer nonlinear programs. Research report RC 23771, IBM T. J. Watson Research Center, Yorktown, NY Bonami P, Lee J, Leyffer S, Waechter A (2011) More branch-and-bound experiments in convex nonlinear integer programming. Technical report ANL/MCS-P1949-0911, Argonne National Laboratory, Mathematics and Computer Science Division, Lemont, IL Bonnans JF, André J (2009) Optimal structure of gas transmission trunklines. Technical report 6791, INRIA Saclay, 91893 ORSAY Cedex, France Bonnard B, Faubourg L, Launay G, Trélat E (2003) Optimal control with state constraints and the space shuttle re-entry problem. J Dyn Control Syst 9(2):155–199 Borghetti A, Frangioni A, Lacalandra F, Nucci CA (2003) Lagrangian heuristics based on disaggregated bundle methods for hydrothermal unit commitment. IEEE Trans Power Syst 18:1–10 Byrd RH, Hribar ME, Nocedal J (1999) An interior point algorithm for large scale nonlinear programming. SIAM J Optim 9(4):877–900 Byrd RH, Gould NIM, Nocedal J, Waltz RA (2004) An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Math Progr Ser B 100(1):27–48 Byrd RH, Nocedal J, Waltz RA (2006) KNITRO: an integrated package for nonlinear optimization. In: di Pillo G, Roma M (eds) Large-scale nonlinear optimization. Springer, New York, pp 35–59 Calamai PH, Moré JJ (1987) Projected gradient methods for linearly constrained problems. Math Progr 39:93–116 Castro J, Gonzalez JA (2004) A nonlinear optimization package for long-term hydrothermal coordination. Eur J Oper Res 154(1):641–658 Chin CM, Fletcher R (2003) On the global convergence of an SLP-filter algorithm that takes EQP steps. Math Progr 96(1):161–177 Coleman TF, Li Y, Verman A (1999) Reconstructing the unknown volatility function. J Comput Finance 2(3):77–102 Conn AR, Gould NIM, Toint PL (1992) LANCELOT: a Fortran package for large-scale nonlinear optimization (release A). Springer, Heidelberg Conn AR, Gould NIM, Toint PL (2000) Trust-region methods. MPS-SIAM series on optimization. SIAM, Philadelphia Cornuejols G, Tütüncü R (2007) Optimization methods in finance. Cambridge University Press, Cambridge Curtis FE, Jiang H, Robinson DP (2015) An adaptive augmented Lagrangian method for large-scale constrained optimization. Math Progr 152(1–2):201–245 Dolan ED, Moré J (2002) Benchmarking optimization software with performance profiles. Math Progr 91(2):201–213 Donde V, Lopez V, Lesieutre B, Pinar A, Yang C, Meza J (2005) Identification of severe multiple contingencies in electric power networks. In: Proceedings 37th North American power symposium, LBNL-57994 Klaus E, Steinbach Marc C (2005) Nonlinear optimization in gas networks. In: Bock HG, Kostina E, Phu HX, Ranacher R (eds) Modeling, simulation and optimization of complex processes. Springer, Berlin, pp 139–148 Fletcher R, Leyffer S (1994) Solving mixed integer nonlinear programs by outer approximation. Math Progr 66:327–349 Fletcher R, Leyffer S (1998) User manual for filterSQP. Numerical analysis report NA/181, University of Dundee Fletcher R, Leyffer S (2002) Nonlinear programming without a penalty function. Math Progr 91:239–270 Fletcher R, Leyffer S (2003) Filter-type algorithms for solving systems of algebraic equations and inequalities. In: di Pillo G, Murli A (eds) High performance algorithms and software for nonlinear optimization. Kluwer, Dordrecht, pp 259–278 Fletcher R, Sainz de la Maza E (1989) Nonlinear programming and nonsmooth optimization by successive linear programming. Math Progr 43:235–256 Fletcher R, Leyffer S, Toint PL (2002) On the global convergence of a filter-SQP algorithm. SIAM J Optim 13(1):44–59 Forsgren A, Gill PE, Wright MH (2002) Interior methods for nonlinear optimization. SIAM Rev 4(4):525–597 Friedlander MP (2002) A globally convergent linearly constrained Lagrangian method for nonlinear optimization. Ph.D. thesis, Stanford University Friedlander MP, Leyffer S (2008) Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs. SIAM J Sci Comput 30(4):1706–1729 Ghaoui LE, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper Res 51(4):509–679 Gill PE, Murray W, Saunders MA (1997) User’s guide for SQOPT 5.3: a Fortran package for large-scale linear and quadratic programming. Technical report NA 97-4, Department of Mathematics, University of California, San Diego Gill PE, Murray W, Saunders MA (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J Optim 12(4):979–1006 Gill PE, Murray W, Saunders MA (2005) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev 47(1):99–131 Gondzio J, Grothey A (2002) Reoptimization with the primal-dual interior point method. SIAM J Optim 13(3):842–864 Gould NIM, Orban D, Toint PL (2015) Cutest: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Comput Optim Appl 60(3):545–557 Goux J-P, Leyffer S (2002) Solving large MINLPs on computational grids. Optim Eng 3:327–346 Huangfu Q, Hall JAJ (2013) Novel update techniques for the revised simplex method. Technical report ERGO-13-001, The School of Mathematics, University of Edinburgh, Edinburgh, UK Kawayir Y, Laird C, Wächter A (2009) Introduction to Ipopt: a tutorial for downloading, installing, and using Ipopt. Manual. IBM T.J. Watson Research Center, Yorktown Heights Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market. Manag Sci 37:519–531 Leyffer S (2001) Integrating SQP and branch-and-bound for mixed integer nonlinear programming. Comput Optim Appl 18:295–309 Leyffer S, Munson TS (2007) A globally convergent filter method for MPECs. Preprint ANL/MCS-P1457-0907, Argonne National Laboratory, Mathematics and Computer Science Division Leyffer S, Lopez-Calva G, Nocedal J (2006) Interior methods for mathematical programs with complementarity constraints. SIAM J Optim 17(1):52–77 Lubin M, Hall JAJ, Petra CG, Anitescu M (2013) Parallel distributed-memory simplex for large-scale stochastic LP problems. Comput Optim Appl 55(3):571–596 Martin A, Möller M, Moritz S (2006) Mixed integer models for the stationary case of gas network optimization. Math Progr 105:563–582 Momoh JA, Koessler RJ, Bond MS, Stott B, Sun D, Papalexopoulos A, Ristanovic P (1997) Challenges to optimal power flow. IEEE Trans Power Syst 12:444–455 Moré JJ, Toraldo G (1991) On the solution of quadratic programming problems with bound constraints. SIAM J Optim 1(1):93–113 Murtagh BA, Saunders MA (1993) MINOS 5.4 user’s guide. Report SOL 83-20R, Department of Operations Research, Stanford University Murtagh BA, Saunders MA (1982) A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints. In: Buckley AG, Goffin J-L (eds) Algorithms for constrained minimization of smooth nonlinear functions, vol 16. Mathematical programming studies, vol 16. Springer, Berlin, pp 84–117 Penfield P, Spence R, Duinker S (1970) Tellegen’s theorem and electrical networks. MIT Press, Cambridge Powell MJD (1978) Algorithms for nonlinear constraints that use Lagrangian functions. Math Progr 14(1):224–248 Rabinowitz G, Mehrez A, Oron G (1988) A nonlinear optimization model of water allocation for hydroelectric energy production and irrigation. Manag Sci 34(8):973–990 Raghunathan A, Biegler LT (2005) An interior point method for mathematical programs with complementarity constraints (MPCCs). SIAM J Optim 15(3):720–750 Sheble GB, Fahd GN (1994) Unit commitment literature synopsis. IEEE Trans Power Syst 9:128–135 Shen C, Leyffer S, Fletcher R (2012) A nonmonotone filter method for nonlinear optimization. Comput Optim Appl 52(3):583–607 Smith E, Hall JAJ (2012) A high performance primal revised simplex solver for row-linked block angular linear programming problems. Technical report ERGO-12-003, The School of Mathematics, University of Edinburgh, Edinburgh, UK Vanderbei RJ, Shanno DF (1999) An interior point algorithm for nonconvex nonlinear programming. COAP 13:231–252 Wächter A, Biegler LT (2005a) Line search filter methods for nonlinear programming: local convergence. SIAM J Optim 16(1):32–48 Wächter A, Biegler LT (2005b) Line search filter methods for nonlinear programming: motivation and global convergence. SIAM J Optim 16(1):1–31 Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Progr 106(1):25–57 Womersley RS, Lau K (1996) Portfolio optimisation problems. In: May RL, Easton AK (eds) Computational techniques and applications: CTAC95. World Scientific Publishing Co., Singapore, pp 795–802 Zhu C, Byrd RH, Lu P, Nocedal J (1997) Algorithm 778: L-BFGS-B—Fortran subroutines for large-scale bound-constrained optimization. ACM Trans Math Softw (TOMS) 23(4):550–560