Practical Piecewise-Linear Approximation for Monotropic Optimization

References

  • Barros O., Weintraub A. Spatial market equilibrium problems and network models. Discrete Applied Mathematics (1986) 13:109–130CrossrefGoogle Scholar
  • Belobaba P., Farkas A. Yield management impacts on airline spill estimation. Transportation Science (1999) 33:217–232LinkGoogle Scholar
  • Ben-Khedher N., Kintanar J., Queille C., Stripling W. Schedule optimization at SNCF: from conception to day of departure. Interfaces (1998) 28:6–23LinkGoogle Scholar
  • Collins M., Cooper L., Helgason R., Kennington J., LeBlanc L. Solving the pipe network analysis problem using optimization techniques. Management Science (1978) 24:747–760LinkGoogle Scholar
  • Conte S.D., de Boor C.Elementary Numerical Analysis: An Algorithmic Approach (1980) 3rd edition(McGraw-Hill, New York) Google Scholar
  • CPLEX Optimization, Inc Using the CPLEX callable library, version 4.0. (1997) (Incline Village, NV)Google Scholar
  • Cross R.G.Revenue Management: Hard-Core Tactics for Market Domination (1997) (Broadway Books, Cambridge, MA) Google Scholar
  • Curry R.E. Optimal airline seat allocation with fare classes nested by origins and destinations. Transportation Science (1990) 24:193–204LinkGoogle Scholar
  • De Boor C.A Practical Guide to Splines (1978) (Springer Verlag, New York) CrossrefGoogle Scholar
  • De Wolf D., Smeers Y. The gas transmission problem solved by an extension of the simplex algorithm. (1999) (SMG, Université Libre de Bruxelles, Belgium) . Technical Report 99/16Google Scholar
  • Dembo R.S., Mulvey J.M., Zenios S.A. Large-scale nonlinear network models and their application. Operations Research (1989) 37:353–372LinkGoogle Scholar
  • Ferguson A.R., Dantzig G.B. The allocation of aircraft to routes—an example of linear programming under uncertain demand. Management Science (1956) 3:45–73LinkGoogle Scholar
  • Fourer R. A simplex algorithm for piecewise-linear programming, III: Computational analysis and applications. Mathematical Programming (1992) 53:213–235CrossrefGoogle Scholar
  • Fourer R., Gay D. Expressing special structures in an algebraic modeling language for mathematical programming. ORSA Journal on Computing (1995) 7:166–190LinkGoogle Scholar
  • Fourer R., Gay D.M., Kernighan B.W.AMPL: A Modeling Language for Mathematical Programming (1993) (The Scientific Press, San Francisco, CA) Google Scholar
  • Fourer R., Marsten R.E. Solving piecewise-linear problems: experiments with a simplex approach. ORSA Journal on Computing (1992) 4:16–31LinkGoogle Scholar
  • Gondzio J. HOPDM (version 2.12)—a fast LP solver based on a primal-dual interior point method. European Journal of Operational Research (1995) 85:221–225CrossrefGoogle Scholar
  • Helgason R.V., Murthy R. A direct simplex algorithm for network flow problems with convex piecewise-linear costs. Optimization Methods and Software (1994) 4:191–207CrossrefGoogle Scholar
  • Ho J.K. Relationships among linear formulations of separable, convex, piecewise-linear problems. Mathematical Programming Study (1985) 24:126–140CrossrefGoogle Scholar
  • Ibaraki T., Katoh N.Resource Allocation Problems: Algorithmic Approaches (1988) (MIT Press, Cambridge, MA) Google Scholar
  • Johnson R.B., Svoboda A.J., Greif C., Vojdani A., Zhuang F. Positioning for a competitive electric industry with PG&E's hydro-thermal optimization model. Interfaces (1998) 28:53–74LinkGoogle Scholar
  • Jung H.-W., Marsten R.E., Saltzman M.J. Numerical factorization methods for interior point algorithms. ORSA Journal on Computing (1994) 6:94–105LinkGoogle Scholar
  • Kamesam P.V., Meyer R.R. Multipoint methods for separable nonlinear networks. Mathematical Programming Study (1984) 22:185–205CrossrefGoogle Scholar
  • Kao C.Y., Meyer R.R. Secant approximation methods for convex optimization. Mathematical Programming Study (1981) 14:143–162CrossrefGoogle Scholar
  • King A.J. Experiences with parallel decomposition using SP/OSL. EKKNEWS 1–2 (1995) (IBM Research, Poughkeepsie, NY) Google Scholar
  • Lustig I.J., Rothberg E. Gigaflops in linear programming. Operations Research Letters (1996) 18:157–165CrossrefGoogle Scholar
  • Mészáros C. The efficient implementation of interior point methods for linear programming and their applications. (1996) (School of Operations Research, Eötvös Loránd University, Budapest, Hungary) . PhD thesisGoogle Scholar
  • Murtagh B.A., Saunders M.A.MINOS 5.4 Release Notes, Appendix to MINOS 5.1 User's Guide, Report SOL 83.20R—1987 (1992) (Stanford University, Stanford, CA) Google Scholar
  • Nash S.G. Nonlinear programming software survey. OR/MS Today (1998) 25:36–45Google Scholar
  • Porteus E.L., Heyman D.P., Sobel M.J. Stochastic inventory theory. Handbooks in OR and MS (1990) 2(North-Holland, Amsterdam) 605–652Google Scholar
  • Rockafellar R.T.Network Flows and Monotropic Optimization (1984) (John Wiley & Sons, New York) Google Scholar
  • Rothberg E., Hendrickson B. Sparse matrix reordering methods for interior point linear programming. INFORMS Journal on Computing (1998) 10:107–113LinkGoogle Scholar
  • Sun J., Tsai K.-H., Qi L., Du D.-Z., Pardalos P.M. A simplex method for network problems with convex separable piecewise-linear costs and its application to stochastic transshipment problems. Network Optimization Problems (1993) (World Scientific Publishing Co., River Edge, NJ) 283–300CrossrefGoogle Scholar
  • Terlaky T.Interior Point Methods in Mathematical Programming (1996) (Kluwer Academic, Dordrecht, The Netherlands) CrossrefGoogle Scholar
  • Thakur L.S. Error analysis for convex separable problems. SIAM Journal of Applied Mathematics (1978) 34:704–714CrossrefGoogle Scholar
  • Trapmann W. Natural gas deliverability model (DELIVER). (1996) . Talk presented at the May INFORMS Conference, Washington, DCGoogle Scholar
  • Vanderbei R.J., Shanno D.F. An interior point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications (1999) 13:231–252CrossrefGoogle Scholar
  • Weatherford L.R., Bodily S.E. A taxonomy and research overview of perishable-asset revenue management: yield management, overbooking and pricing. Operations Research (1992) 40:831–844LinkGoogle Scholar
  • Williamson E.L. Airline network seat inventory control: methodologies and revenue impacts. (1992) (Flight Transportation Lab, Department of Aeronautics and Astronautics, MIT, Cambridge, MA) . Technical Report R92-3Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.