Arrival Rate Approximation by Nonnegative Cubic Splines

References

• Alizadeh F., Goldfarb D. Second-order cone programming. Math. Programming (2003) 95(1):3–51Crossref, Google Scholar
• Benson H. Y., Vanderbei R. J., Shanno D. F. Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions. Comput. Optim. Appl. (2002) 23(2):257–272Crossref, Google Scholar
• Byrd R. M., Hribar M. E., Nocedal J. An interior point method for large scale nonlinear programming. SIAM J. Optim. (1999) 9(4):877–900Crossref, Google Scholar
• Czyzyk J., Mesnier M., Moré J. The NEOS server. IEEE J. Comput. Sci. Engrg. (1998) 5(3):68–75Crossref, Google Scholar
• de Boor C.A Practical Guide to Splines (1978) (Springer-Verlag, New York) Crossref, Google Scholar
• Dette H., Studden W. J.The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis (1997) (Wiley, New York) Google Scholar
• Dolan E. The NEOS server 4.0 administrative guide. (2001) . Technical Report ANL/MCS-TM-250, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILGoogle Scholar
• Faybusovich L. Self-concordant barriers for cones generated by Chebychev systems. SIAM J. Optim. (2002) 12(3):770–781Crossref, Google Scholar
• Fourer R., Gay D. M., Kernighan B. W.AMPL: A Modeling Language for Mathematical Programming (2002) 2nd ed.(Boyd and Fraser, Danvers, MA) Google Scholar
• Gal A., Eckstein J. Managing periodically updated data in relational databases: A stochastic modeling approach. J. ACM (2001) 46(6):1141–1183Crossref, Google Scholar
• Gal A., Eckstein J., Stoumbos Z. Scheduling of data transcription in periodically connected databases. Stochastic Anal. Appl. (2003) 21(5):1021–1058Crossref, Google Scholar
• Gropp W., Moré J., Buhman M. D., Iserles A. Optimization environments and the NEOS server. Approximation Theory and Optimization (1997) (Cambridge University Press, Cambridge, UK) 167–182Google Scholar
• Karlin S., Studden W. J.Tchebycheff Systems, with Applications in Analysis and Statistics (1966) (Wiley, New York) Google Scholar
• Kuhl M. E., Bhairgond P. S. New frontiers in input modeling: Nonparametric estimation of nonhomogeneous Poisson process using wavelets. Proc. 2000 Winter Simulation Conf. (2000) Orlando, FL:562–571Crossref, Google Scholar
• Kuhl M. E., Wilson J. R. Modeling and simulating Poisson processes having trends or nontrigonometric cyclic effects. Eur. J. Oper. Res. (2001) 133(3):566–582Crossref, Google Scholar
• Kuhl M. E., Damerdji H., Wilson J. R. Least squares estimation of nonhomogeneous Poisson processes. Proc. 1998 Winter Simulation Conf. (1998) Washington, D.C.:637–646Crossref, Google Scholar
• Kuhl M. E., Sumant S. G., Wilson J. R. An automated multiresolution procedure for modeling complex arrival processes. INFORMS J. Comput. (2006) 18(1):3–18Link, Google Scholar
• Kuhl M. E., Wilson J. R., Johnson M. A. Estimating and simulating Poisson processes having trends or multiple periodicities. IIE Trans. (1997) 29(3):201–211Crossref, Google Scholar
• Lewis P. A. W., Shedler G. S. Simulation of nonhomogeneous Poisson processes by thinning. Naval Res. Logist. Quart. (1979) 26(3):403–413Crossref, Google Scholar
• Nemirovski A. What can be expressed via conic quadratic and semidefinite programming? (1999) . Weekly seminar, RUTCOR, Rutgers University, Piscataway, NJGoogle Scholar
• Nesterov Y., Frenk J. B. G., Roos C., Terlaky T., Zhang S. Squared functional systems and optimization problems. High Performance Optimization (2000) (Kluwer, Dordrecht, The Netherlands) 405–440Crossref, Google Scholar
• Nesterov Y., Nemirovski A.Interior Point Polynomial Methods in Convex Programming: Theory and Applications (1994) (SIAM, Philadelphia, PA) Crossref, Google Scholar
• Nocedal J., Waltz R. A. KNITRO user's manual. (2003) . Technical Report OTC 2003/05, Optimization Technology Center, Northwestern University, Evanston, ILGoogle Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Schumaker L. L.Spline Functions: Basic Theory (1981) (Wiley, New York) Google Scholar
• Scott D. W. Nonparametric probability density estimation by optimization theoretic techniques. (1976) . Ph.D. thesis, Rice University, Houston, TXGoogle Scholar
• Scott D. W., Tapia R. A., Thompson J. R. Nonparametric probability density estimation by discrete maximum penalized-likelihood criteria. Ann. Statist. (1980) 8(4):820–832Crossref, Google Scholar
• Shao J. Linear model selection by cross-validation. J. Amer. Statist. Assoc. (1993) 88:486–494Crossref, Google Scholar
• Thompson J. R., Tapia R. A.Nonparametric Function Estimation, Modeling, and Simulation (1990) (SIAM, Philadelphia, PA) Crossref, Google Scholar
• Wächter A., Biegler L. T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programming (2006) 106(1):25–57Crossref, Google Scholar
• Wahba G.Spline Models for Observational Data (1990) (SIAM, Philadelphia, PA) Crossref, Google Scholar
• Walter G. G., Shen X. Positive estimation with wavelets. Wavelets, Multiwavelets, and Their Applications. Contemporary Mathematics (1998) 216(American Mathematical Society, Providence, RI) 63–79Crossref, Google Scholar
• Wolkowicz H., Saigal R., Vandenberghe L.Handbook of Semidefinite Programming: Theory, Algorithms and Applications (2000) (Kluwer, Dordrecht, The Netherlands) Crossref, Google Scholar