Optimization applied on regulatory and eco-finance networks -survey and new developments

Pacific Journal of Optimization

Volumn 6, Issue 2, 2010, Pages 319-340

  Weber, Gerhard Wilhelm ^a,b,c,d   Kropat, Erik ^e   Tezel, Aysun ^a   Belen, Selma ^f  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^b UNIVERSITY OF SIEGEN   (Germany)

^c UNIVERSITY OF AVEIRO   (Portugal)

^d UNIVERSITI TEKNOLOGI MALAYSIA   (Malaysia)

^e BUNDESWEHR UNIVERSITY MUNICH   (Germany)

^f CAG UNIVERSITY   (Turkey)

Author keywords

Eco finance networks; Gene environment networks; Generalized semi infinite programming; Regulatory networks; Spline regression; Stochastic differential equations; Uncertainty

Indexed keywords

EID: 79951494291     PISSN: 13489151     EISSN: 13498169     Source Type: Journal    
DOI: None     Document Type: Article

References (69)

1. M.U. Akhmet, J. Gebert, M. Lätsch, S.W. Pickl, G.-W. Weber and R. Wünschiers, Algorithmic computational biology: stability analysis of gene-expression patterns, Journal of Computational Technologies 9 (2004).
2. M.U. Akhmet, J. Gebert, H. Ö ktem, S.W. Pickl and G.-W. Weber, An improved algorithm for analytical modeling and anticipation of gene expression patterns, Journal of Computational Technologies 10 (2005) 3-20.
3. B. Akteke-Öztürk and G.-W. Weber, A survey and results on semidefinite and nonsmooth optimization for minimum sum of squared distances problem, Middle East Technical University, Institute of Applied Mathematics, Preprint 65 (2006).
4. B. Akteke-Öztürk, G.-W. Weber and E. Kropat, Continuous optimization approaches for clustering via minimum sum of squares, in The 20th International Conference, EURO Mini Conference "Continuous Optimization and Knowledge-Based Technologies"(EurOPT-2008), L. Sakalauskas, G.-W.Weber and E. K. Zavadskas (eds.), Vilnius Gediminas Technical University Publishing House"Technika", 2008, pp. 253-258.
5. H. Amann, Gewöhnliche Differentialgleichungen, Walter de Gruyter, Berlin, New York,
6. A. Aster, B. Borchers and C. Thurber, Parameter estimation and inverse problems, Academic Press, Amsterdam, 2004.
7. L.M. Brègman, The method of successive projection for finding a common point of convex sets, Soviet. Math. Dokl. 6 (1965) 688-692.
8. W. Briec and B. Solonandrasana, Some remarks on a successive projection sequence, preprint, University of Perpignan (2006).
9. T. Bröcker and L. Lander, Differentiable Germs and Catastrophes, London Mathematical Society Lecture Note Series 17, Cambridge University Press, London, 1975.
10. T. Chen, H.L. He and G.M. Church, Modeling gene expression with differential equations, Proc. Pacific Symposium on Biocomputing (1999) 29-40.
11. W.D. Collins and C. Hu, Fuzzily determined interval matrix games, http://www-bisc.cs.berkeley.edu/BISCSE2005/Abstracts_Proceeding/Friday/FM3/Chenyi_Hu.pdf
12. D.M. Dubois and E. Kalisz, Precision and stability of Euler, Runga-Kutta and incursive algorithm for the harmonic oscillator, International Journal of Computing Anticipatory Systems 14 (2004) 21-36.
13. T. Ergenç and G.-W. Weber, Modeling and prediction of gene-expression patterns reconsidered with Runge-Kutta discretization, Journal of Computational Technologies 9 (2004) 40-48.
14. M. Fiedler, J. Nedoma, J. Ramik, J. Rohn and K. Zimmermann, Linear optimization problems with inexact data, Springer Verlag, Berlin, 2006.
15. J.H. Friedman, Multivariate Adaptive Regression Splines, The Annals of Statistics 19 (1991) 1-67.
16. J. Gebert, M. Lätsch, S.W. Pickl, N. Radde, G.-W. Weber and R. Wünschiers, Genetic networks and anticipation of gene expression patterns, AIP Conference Proceedings 718 (2004) 474-485.
17. J. Gebert, M. Lätsch, S.W. Pickl, G.-W. Weber and R. Wünschiers, An algorithm to analyze stability of gene-expression pattern, Discrete Applied Mathematics 154 (2006) 1140-1156.
18. J. Gebert, M. Lätsch, E.M.P. Quek and G.-W.Weber, Analyzing and optimizing genetic network structure via path-finding, Journal of Computational Technologies 9 (2004) 3-12.
19. J. Gebert, H. Öktem, S.W. Pickl, N. Radde, G.-W. Weber and F.B. Yilmaz, Inference of gene expression patterns by using a hybrid system formulation -an algorithmic approach to local state transition matrices, in Anticipative and predictive models in systems science I, G.E. Lasker and D.M. Dubois (eds.), IIAS. Windsor, Ontario, 2004, pp. 63-66.
20. J. Gebert, N. Radde and G.-W. Weber, Modelling gene regulatory networks with piecewise linear differential equations, European J. Oper. Res. 181 (2006) 1148-1165.
21. T. Hastie, R. Tibshirani and J.H. Friedman, The Elements of Statistical Learning -Data Mining, Inference and Prediction, Springer, New York, 2001.
22. M.D. Hoon, S. Imoto, K. Kobayashi, N. Ogasawara and S. Miyano, Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using differential equations, Pac. Symp. Biocomput. (2003) 17-28.
23. A. Işcanoǧlu, G.-W. Weber and P. Taylan, Predicting Default Probabilities with Generalized Additive Models for Emerging Markets, invited Lecture, Graduate Summer School on New Advances in Statistics, METU, August 11-24, 2007, http://144.122.137.55/gweber/.
24. H.T. Jongen, P. Jonker and F. Twilt, Nonlinear Optimization in Finite Dimensions -Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects, Kluwer Academic Publishers, Boston, 2000.
25. H.T. Jongen and G.-W. Weber, On parametric nonlinear programming, Ann. Oper. Res. 27 (1990) 253-284.
26. H.T. Jongen and G.-W. Weber, Nonlinear optimization: characterization of structural stability, J. Global Optim. 1 (1991) 47-64.
27. M. Kahraman, H. Öktem, G.-W.Weber and M. Akhmet, Using piecewise linear systems with delay to grab the functional dynamics in biological systems, in Proceedings of International Symposium on Health Informatics and Bioinformatics, U. Sezerman (ed.), Sabanci University, 2008.
28. P.E. Kloeden, E. Platen and H. Schurz, Numerical Solution of SDE Through Computer Experiments, Springer Verlag, New York, 1994.
29. A. Kurzhanski and I. Vályi, Ellipsoidal Calculus for Estimation and Control, Birkhäuser, Boston, 1996.
30. D. Lozovanu, S.W. Pickl and G.-W. Weber, Optimization, monotonicity and the determination of Nash equilibria -an algorithmic analysis, in AIP Conference Proceedings 718 (2004) 351-361.
31. R.E. Moore, Interval Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1966.
32. R.E. Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979.
33. A. Nemirovski, Five lectures on modern convex optimization, http://iew3.technion.ac.il/Labs/Opt/opt/LN/Final.pdf.
34. A. Nemirovski, Lectures on modern convex optimization, Israel Institute of Technology (2002) http://iew3.technion.ac.il/Labs/Opt/opt/LN/Final.pdf.
35. Y.E. Nesterov and A.S. Nemirovskii, Interior Point Methods in Convex Programming, SIAM, Philadelphia, 1993.
36. S. Pickl, Der τ -value als Kontrollparameter -Modellierung und Analyse eines Joint-Implementation Programmes mithilfe der dynamischen kooperativen Spieltheorie und der diskreten Optimierung, thesis, Darmstadt University of Technology, Department of Mathematics, 1998.
37. S. Pickl, Convex games and feasible sets in control theory, Mathematical Methods of Operations Research 53 (2001) 51-66.
38. S. Pickl, An iterative solution to the nonlinear time-discrete TEM model -the occurence of chaos and a control theoretic algorithmic approach, AIP Conference Proceedings 627 (2002) 196-205.
39. S. Pickl, An algorithmic solution for an optimal decision making process within emission trading markets, Annales du Lamsade No.3, Laboratoire d'Analyse et Modèlisation de Systemes pour l'Aide a la Décision, University Lamsade, Paris, France.
40. K. Ramadan, Linear Programming with Interval Coefficients, Carleton University, Ottawa, Ontario, 1996.
41. E. Sakamoto and H. Iba, Inferring a system of differential equations for a gene regulatory network by using genetic programming, in Proc. Congress on Evolutionary Computation, 2001, pp. 720-726.
42. T. Shaocheng, Interval number and fuzzy number linear programmings, Fuzzy Sets and Systems 66 (1994) 301-306.
43. M. Taştan, Analysis and prediction of gene expression patterns by dynamical systems, and by a combinatorial algorithm, Institute of Applied Mathematics, METU, MSc Thesis, 2005.
44. M. Taştan, T. Ergeņc, S.W. Pickl and G.-W. Weber, Stability analysis of gene expression patterns by dynamical systems and a combinatorial algorithm, preprint, Informatics Institute, METU, Ankara (2005).
45. M. Taştan, S.W. Pickl and G.-W. Weber, Mathematical modeling and stability analysis of gene-expression patterns in an extended space and with Runge-Kutta discretization, in Proceedings of Operations Research, Springer, Berlin, Heidelberg, 2005, pp. 443-450.
46. P. Taylan and G.-W. Weber, Approximation of stochastic differential equations by additive models using splines and conic programming, in Proceedings of CASYS'07, Eighth International Conference on Computing Anticipatory Systems, D.M. Dubois (ed.), Liege, Belgium, 2007.
47. P. Taylan and G.-W. Weber, New approaches to regression in financial mathematics by additive models, Journal of Computational Technologies 12 (2007) 3-22.
48. P. Taylan and G.-W. Weber, Organization in finance prepared by stochastic differential equations with additive and nonlinear models and continuous optimization, Organizacija (Organization -Journal of Management, Information Systems and Human Resources) 41 (2008) 185-193.
49. P. Taylan, G.-W. Weber and A. Beck, New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and techology, Optimization 56 (2007) 675-698.
50. P. Taylan, G.-W. Weber, L. Liu and F. Yerlikaya, On foundations of parameter estimation for generalized partial linear models with B-splines and continuous optimization, to appear in Computers and Mathematics with Applications.
51. P. Taylan, G.-W. Weber and F. Yerlikaya, Continuous optimization applied in MARS for modern applications in finance, science and technology, in The 20th International Conference, EURO Mini Conference"Continuous Optimization and Knowledge-Based Technologies" (EurOPT-2008), L. Sakalauskas, G.-W. Weber and E. K. Zavadskas (eds.), Vilnius Gediminas Technical University Publishing House "Technika", 2008, pp. 317-322.
52. A. Tomasgard and K.T. Midthun, Stochastic programming and natural gas -A modelling perspective, http://www.univie.ac.at/spxi/tutorial/TutPresTomasgard.pdf
53. Ö. Uǧur, S.W. Pickl, G.-W. Weber and R. Wünschiers, An algorithmic approach to analyze genetic networks and biological energy production: an introduction and contribution where OR meets biology, Optimization 58 (2009) 1-22.
54. Ö. Uǧur and G.-W. Weber, Optimization and dynamics of gene-environment networks with intervals, Journal of Industrial Management and Optimization 3 (2007) 357-379.
55. J. von Neumann, Functional Operators, Vol. II. The Geometry of Orthogonal Spaces, Princeton University Press, Princeton NJ, 1950; Ann. Math. Stud. 22, reprint of mimeographed lecture notes first distributed in 1933.
56. G.-W. Weber, Charakterisierung struktureller Stabilität in der nichtlinearen Optimierung, in Aachener Beiträge zur Mathematik 5, H.H. Bock, H.T. Jongen and W. Plesken (eds.), Augustinus publishing house (now: Mainz publishing house) Aachen, 1992.
57. G.-W.Weber, Generalized semi-infinite optimization: on iteration procedures and topological aspects, in Similarity Methods, B. Kröplin, S. Rudolph, S. Brückner (eds.), University of Stuttgart, 1998, pp. 281-309.
58. G.-W. Weber, Generalized semi-infinite optimization: on some foundations, Journal of Computational Technologies 4 (1999) 41-61.
59. G.-W. Weber, Generalized Semi-Infinite Optimization and Related Topics, Heldermann Publishing House, Research and Exposition in Mathematics 29, Lemgo, 2003.
60. G.-W. Weber, S.Z. Alparslan-Gök and N. Dikmen, Environmental and life sciences: gene-environment networks -optimization, games and control -a survey on recent achievements, Journal of Organisational Transformation and Social Change 5 (2008) 197-233.
61. G.-W. Weber, S.Z. Alparslan-Gök and B. Söyler, A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics, Environmental Modeling & Assessment 14 (2009) 267-288.
62. G.-W. Weber, E. Kropat, B. Akteke-Öztürk and Z.K. Görgülü, A survey on OR and mathematical methods applied on gene-environment networks, Cent. Eur. J. Oper. Res. 17 (2009) 315-341.
63. G.-W. Weber, P. Taylan, S.Z. Alparslan-Gök, S. Özöǧür and B. Akteke-Öztürk, Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation, in TOP, the Operational Research journal of SEIO (Spanish Statistics and Operations Research Society) 16 (2008) 284-318.
64. G.-W. Weber and A. Tezel, On generalized semi-infinite optimization of genetic networks, TOP 15 (2007) 65-77.
65. G.-W. Weber, A. Tezel, P. Taylan, A. Soyler and M. Çetin, Mathematical contributions to dynamics and optimization of gene-environment networks, Optimization 57 (2008) 353-377.
66. G.-W. Weber, Ö. Uǧur, P. Taylan and A. Tezel, On optimization, dynamics and uncertainty: a tutorial for gene-environment networks, Discrete Applied Mathematics 157 (2009) 2494-2513.
67. F. Yerlikaya, G.-W.Weber, I. Batmaz, G. Köksal and P. Taylan, MARS Algoritmasi{dotless}nda Tikhonov düzenlemesi veçok amaçli optimizasyon kullanimi, Galatasaray University, Istanbul, Turkey, 2008.
68. F.B. Yilmaz, A mathematical modeling and approximation of gene expression patterns by linear and quadratic regulatory relations and analysis of gene networks, Institute of Applied Mathematics, METU, MSc Thesis, 2004.
69. F.B. Yilmaz, H. Öktem and G.-W. Weber, Mathematical modeling and approximation of gene expression patterns and gene networks, in Operations Research Proceedings, F. Fleuren, D. den Hertog and P. Kort (eds.), 2005, pp. 280-287.