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Details of project

  
Identifier
43276
Type K
Principal investigator Rapcsák, Tamás
Title in Hungarian A dötéstámogatás modern matematikai eszközei
Title in English Modern mathematical tools for decision support systems
Panel Mathematics and Computing Science
Department or equivalent HUN-REN Institute for Computer Science and Control
Participants Balla, Katalin
Bozóki, Sándor
Csáki, Péter
Fülöp, János
Gerencsérné Vágó, Zsuzsanna
Kéri, Gerzson
Márton, Sándor
Mészáros, Csaba
Michaletzky, György
Molnár, Márk
Németh, Sándor Zoltán
Prill, Mária
Starting date 2003-01-01
Closing date 2007-12-31
Funding (in million HUF) 16.518
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
Két nagy tématerületen értünk el eredményeket: 1. a többszempontú döntési problémákban és 2. az optimalizáláselméletben. 1. Kiemelendők a páros összehasonlítás mátrixokkal kapcsolatos eredmények, a légkörbe jutó gázok mennyiségének csökkentésére vonatkozó tárgyalások játékelméleti modellezése és a budapesti 4-es metró útvonal alternativáinak összehasonlító vizsgálata térbeli többszempontú csoportos döntési modell alapján. 2. Kiemelendő eredmények a Samuelson 1938-ból származó kinyilvánított preferencia problémájának megoldása folytonosan differenciálható kereslet függvény esetén, Fenchel 1953-ból származó nívóhalmaz problémájának megoldása, a Stiefel sokaságokon történú optimalizálás strukturális vizsgálata, a skaláris derivált bevezetése és alkalmazása fixponttételek általánosítására, variációs egyenlőtlenségek, integrálegyenletek és Riemann geometriai feladatok megoldására, hatékony belsőpontos algoritmusok tervezése és implementálása, továbbá, többdimenziós diszkrét (Hamming) terek adott sugárral történő lefedését biztosító halmazok keresése.
Results in English
Our results belong to two research directions: 1. multiattribute decision problems and 2. optimization theory. 1. Important results are related to pairwise comparison matrices, the game theoretical modelling of discussions on decreasing the transmission of gases causing greenhouse effects into the atmosphere, and the comparative analysis of the alternatives of the line Metro4 in Budapest. 2. Important results are the solution of the revealed preference problem in the case of a continuously differentiable demand function originated from Samuelson in (1938), the solution of the level set problem of Fenchel (1953) in the smooth case, some structural characterizations of optimization on Stiefel manifolds, the introduction of the notion "scalar derivative" and its applications to generalization of fixed point theorems, solution of variational inequalities, integral equalities and Riemann geometrical problems, the planning and implementation of efficient interior point algorithms and the covering of multidimensional discrete (Hamming) spaces by codes with a given radius.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=43276
Decision
Yes





 

List of publications

  
Kéri, G.: Types of superregular matrices and the number of n-arcs and complete n-arcs in PG(r,q), Journal of Combinational Designes 14 pp. 336-390, 2006
Kéri, G.: The number of inequivalent (2R+3,7)R optimal covering codes, Journal of Integer Sequences 9 pp.1-8, 2006
Abramov, A. A. - Balla, K. - Uljanova, V. I. - Yukhno. L. SZ.: Nelinejnaya samos opriyazhennaja spektaral'naya zadacsa dlya differencial'no-algebraicheszkih uravnenij, Differencial'nye uravnenniya 39 (7) pp. 867-878, 2003
Abramov, A. A. - Balla, K. - Uljanova, V. I. - Yukhno, L. Sz.: A nonlinear self-adjoint spectral problem for differential-algebraic equation, Differential Equations 39 (7) pp. 913-925, 2003
Balla, K. - Linh, V. H.: Adjoint pairs of differential-algebraic equations and Halmiltonian Systems, Applied Numerical Mathematics 53 pp. 131-148, 2005
Balla, K. - Márton, S. - Rapcsák, T.: Air pollution modeling in action, Advancing in Air Pollution Modleing for Environmental Security. Nato Science Series. IV. Earth and Environmental Science-Vol. 54-Springer, 2005
Balla, K. - Marz, R.: Linear boundary value for differential algebraic equations, Preprint Nr. 2003-7. Humboldt-Universität zu Berlin.Mathematisch-Naturwissenschaftliche Fakultät II., Institut für Mathematik, 2003
Balla, K. - Marz, R.: Index criteria for differential algebraic equations arising from linear-quadratic optimal control problems, Preprint Nr.2003-14. Humboldt Universitat zu Berlin.Mathematisch-Naturwiss.Fak.II.Inst.für Math. p. 25, 2003
Balla, K. - Marz, R.: Linear boundary value for differential algebraic equations, Miskolc Mathematical Notes 5 (1) pp. 3-18, 2004
Balogh, J. - Csendes, T. - Rapcsák, T.: Some global optimization problems on Stiefel manifolds, Journal of Global Optimization 30 pp. 91-101, 2004
Balogh, J. - Csendes, T. - Rapcsák, T.: Globális optimalizálás Stiefel sokaságokon - egy érdekes diszkretizálási eredmény, Alkalmazott Matematikai Lapok 22 pp. 163-176, 2005
Bárdosi, V. - Kiss, G. - Kiss, M. - Rapcsák, T.: Kísérlet magyar szavak jelentéshasonlóságának meghatározására a Magyar szókincstár segítségével, II. Magyar Számítógépes Nyelvészeti Konferencia Kiadványa, 2004
Bozóki, S.: A method for solving LSM problems for small size in the AHP, Central European Journal of Operations Research 11 pp. 17-33, 2003
Bozóki, S.: Súlyok meghatározása páros összehasonlítása mátrixok legkisebb négyzetes közelítése alapján, Alkalmazott Matematikai Lapok 23 pp. 121-137, 2006
Bozóki, S. - Lewis, R. H.: Solving the least square method problem in the AHP for 3X3 and 4X4 matrices, Central European Journal of Operations Research 13 pp. 17-33, 2005
Cushing, J. B. - Wilson, T. - Fülöp, J.: Eco-informatics for decision makers, Advancing a Research Agenda. In: L.Rashid and B.Ludaescher (eds). Lecture Notes in Comp. Sci. Subseries: Lecture Notes in Bioinform. Proc. of the 2nd Int. Workshop on DA, 2005
Cushing, J. B. - Wilson, T. - Fülöp, J.: Eco-informatics and natural resourrce management, In: ACM international Conference Prec. Series 89 pp. 211-212, 2005
da Cruz Neto, J. X. - Ferreira, P. P. - Lucambio Pérez, L. R. - Németh, S. Z.: Convex- and monotone-transformable mathematical programming problems and a proximal-like method, Journal of Global Optimization 35 pp. 53-69, 2006
Ekárt, A. - Németh, S. Z.: Stability analysis of tree structured decision functions, European Journal of Operational Research. 160 pp. 676-695, 2005
Ferreira, O. P. – Németh, S. Z. – Lucambio Pérez, L. R.: Singularities of monotone vector fields and an extragradient-type algorithm, Journal of Global Optimization 31 pp. 133-151, 2005
Forgó, F. - Fülöp, J. - Prill, M.: Game theoretical models for climate change negotiations, European Journal of Operational Research 160 pp. 252-267, 2005
Fülöp, J. - Roth, J. - Schweik, C.: Decision making in the context of eco-infomratics, In: Cushing, J. and Wilson, T. (eds) Eco-Informatics for Decision Makers: Advancing a Research Agenda. Report of an NSH-and USGS/NBII-sponsored Workshop on Eco Informat, 2005
Gass, S. I.– Rapcsák, T.: Singular value decomposition in AHP, European Journal of Operational Research 154 (3) pp. 573-584, 2004
Gerencsér, L. - Michaletzky, Gy.: Risk sensitive identification of ARMA processes, In: Lecture Notes in Control and Information Sciences.286. Directions in Mathematical Systems Theory and Optimization (eds: A.Rantzer, C.I.Barnes) Springer pp. 141-157, 2003
Gerencsér, L. - Rásonyi, M. - Vágó, Zs.: Controlled Lyapunov exponents in finance, biology and optimization, In: Proceedings of the European Control Conference, ECC 2003, Cambridge, September 1-4, 2003
Gerencsér, L. - Rásonyi, M. - Vágó, Zs.: Controlled Lyapunov exponents in finance, biology and optimization, In: Proceedings of the 11th Mediterranean Conference on Control and Automation, MED'03, T7-054, Rhodes, June 18-20, 2003. CD, 2003
Gerencsér, L. - Molnár-Sáska, G. - Michaletzky, Gy. - Tusnády, G. - Vágó, Zs.: Rejtett Markov modellek. III.rész. (Hidden Markov models. Lecture Notes in Hungarian), Egyetemi jegyzetek, 2004
Gombani, A. - Michaletzky, Gy.: On the Nevanlinna-Pick interpolation problem:analysis of the McMillan-degree, REPORT No.30.2002/2003.-SE+spring. Institute MITTAG-LEFELER, The Royal Swedisch Academy of Sciences Pub, 2003
Gombani, A. - Michaletzky, Gy.: On the parametrization of Suhr-and positive real functions of degree n with fixed interpolating conditions, REPORT No.31.2002/2003.-SE+spring.ISSN 1103-467X.ISNR IML-R-31-02-03. Institute MITTAG-LEFELER, The Royal Swedisch Academy of Sciences Pub, 2003
Gyöngyi, I. - Michaletzky, Gy.: On the Wong-Zakai approximations with delta martingales, Proc.R.Soc.London,A. 460 pp. 309-324, 2003
Isac, G. - Németh, S. Z.: Scalar derivatives and asymptotic scalar derivatives. Properties and some applications, Journal of Mathematical Analysis and Applications 278 pp. 149-170, 2003
Isac, G. - Németh, S. Z.: Scalar derivatives and scalar asymptotic derrivatives. An Altman type fixed point theorem on convex cones and some applications, Journal of Mathematical Analysis and Applications 290 pp. 452-468, 2004
Isac, G. - Németh, S.Z.: Scalar derivatives, asymptotic scalar derivatives and their applications, Kluwer Academic Publishers.(accepted), 2008
Kéri, G. - Kisvölcsey, Á.: On Computing in the Hamming distance, Acta Cybernetica 40 pp. 243-256, 2003
Kéri, G. - Östergard, P.R.J.: On the covering radius of small codes, Studia Scientiarium Mathematicarum Hungarica 40 pp. 243-256, 2003
Kéri, G.: Classification of MDS codes by exchaustive computer search, In: 6th International Conference on Applied Informatics. (Eger, Hungary, January 27-31, 2005), 2005
Kéri, G. - Östergard, P. R. J.: Bounds covering codes over large alphabets, Design, Codes and Cryptography 37 pp. 45-60, 2005
Márton, S. - Rapcsák, T.: Air pollution transmissions - case studies, Central European Journal of Operations Research 13 pp. 271-278, 2005
Mészáros, Cs.: On the Cholesky factorization in interior point methods, Computers and Mathematics with Applications 50 pp. 1157-1166, 2005
Mészáros, Cs.: On the performance of the Cholesky factorization in interior point methods on Pentium 4 processors, Central European Journal of Operations Research 13 pp. 289-298, 2005
Mészáros, Cs.: Sparsity in convex quadratic programming with interior point methods, Optimization Methods and Software 21 (5) pp. 733-745, 2006
Mészáros, Cs. - Rapcsák, T.: A remark on: Rudolf Vetschera,''Strict preference and sensitivity analysis in addictive utility functions with interval data, Central European Journal of Operations Research 13 pp. 209-210, 2005
Mészáros, Cs. - Suhl, U. H.: Advanced preprocessing techniqques for linear and quadratic problems, OR SPECTRUM 25 pp. 557-595, 2003
Michaletzky, Gy.: Quasi-similarity of compressed shift operators, Acta Sci. Math. 69 pp. 223-239, 2003
Mihályi, B. - Tardy, J. - Végh, M. - Zentai, L.: National ecological networks of European countries, ELTE Térképtudományi és Geoinformatikai Tanszék, 2005
Mihályi, B.: Galamboktól a repülőgépekig, Geodézia és Kartográfia 12 pp. 32-34, 2004
Mihályi, B.: Madridi ICA szeminárium, Geodézia és Kartográfia 10 p. 42, 2005
Mihályi, B.: Térképek a weben, Geodézia és Kartográfia 3 pp. 37-38, 2005
Mihályi, B.: Webes történelmi atlasz, Geodézia és Kartográfia 2 pp. 37-38, 2005
Mihályi, B.: Göring atlasz, Geodézia és Kartográfia 1 pp. 39-40, 2005
Mihályi, B.: Military history in educational atlases, In: ICA joint seminar (Internet-based cartographic teaching and learning: Atlases, map use and visual analytics) proceedings. pp. 119-125, 2005
Mihályi, B.: The role of maps in the battle of the Budapest 1944-45, In: 21st Conference on the History of Cartography proceedings. p. 109, 2005
Mihályi, B.: Történelmi térképek szerepe az érettségi tükrében, Térinformatika 6 pp. 37-38, 2005
Mihályi, B.: Térinformatika az ICA konferencián, Geodézia és Kartográfia 7 pp. 26-27, 2005
Mihályi, B.: Második világháborús objektum- és esemény-rekonstrukció, Acta Agraria Kaposvariaensis pp. 35-61, 2005
Mihályi, B. - Tardy, J. – Végh, M. – Zentai, L.: National ecological networks of European countries, ELTE Térképtudományi és Geoinformatikai Tanszék, 2005
Németh, S. Z.: Variational inequalities on Hadamard manifolds, Nonlinear Analysis, Theory and Applications 52 pp. 1491-1498, 2003
Németh, S. Z.: Scalar derivatives in Hilbert spaces, Positivity 10 (2) 299-314, 2006
Németh, S. Z. – Rapcsák, T. – Temesi, J.: Evaluation of tenders for developing the economy, Central European Journal of Operations Research 13 pp. 299-317, 2005
Rapcsák, T.: Mechanical equilibrium and equilibrium systems, In: Equilibrium problems and variational models eds.: (P.Daniele), F. Giannessi and A. Maugeri. Kluwer Academic Publishers. pp. 379-399, 2003
Rapcsák, T.: Some optimization problems in statistics, Journal of Global Optimization 28 pp. 217-228, 2004
Rapcsák, T.: Survey on the Fenchel problem of level sets, In: Variational analysis and applications. eds.: F. Giannessi and A. Maugeri, Kluwer Academic Publishers, Boston pp. 935-950, 2005
Rapcsák, T.: Local convexity on smooth manifolds, Journal of Optimization Theory and Applications 127 p. 165-176, 2005
Rapcsák, T.: Fenchel problem of level sets, Journal of Optimization Theory and Applications 127 pp. 177-191, 2005
Abramov, A. A. - Balla, K. - Uljanova, V. I. - Yukhno, L. Sz.: O nelinejnoj samos opryazhennoj spektral'noj zadache dlya odnogo klassa diferencial'no-algebraicheskih uravnenij, Zsurnal Víchislitel'noj Matematiki i Matematicheskoj Fiziki 43 (3) pp. 410-421, 2003
Crouzeix, J. P. - Rapcsák, T.: Integrability of pseudomonotone differentiable maps and revealed preference problem, Journal of Convex Analysis 12 (2) pp. 431-446, 2005
Isac, G. - Németh, S. Z.: Fixed points and positive eigenvalues for nonlinear operators, Journal of Mathematical Analysis and Applications 314 pp. 500-512, 2006
Kéri, G. - Östergard, R.J.: Further results on the covering radius of small codes, Discrete Mathematics 307 pp. 69-77, 2007
Kéri, G.: Kritériumok páros összehasonlítás mátrixokra, Szigma 36 pp. 139-148, 2006
Rapcsák, T.: Martos Béla optimalizáláselméleti munkásságának méltatása az Egerváry emlékplakett átadása alkalmából, Alkalmazott Matematikai Lapok 23 pp. 1-4, 2006
Rapcsák, T.: Nemlineáris optimalizálás, Aula Kiadó, 2006
Isac, G. - Németh, S. Z.: Duality of nonlinear complementarity problems by using inversions and scalar derivatives, Mathematical Inequalities and Applications 9 (4) pp. 781-795, 2006
Németh, A. B. - Németh, S. Z.: How to compare the incomparable - The Pareto model and the multiobjective decision making, School of Mathematics, The University of Birmingham, Preprint 2006/9, 2006
Isac, G. - Németh, S. Z.: Duality of implicit complementarity problems by using inversions and scalar derivatives, Journal of Optimization Theory and Applications 128 (3) 621-633, 2007
Isac, G. - Németh, S. Z.: REFE-acceptable mappings: A necessary and sufficient condition for the nonexistence of a regular expectional family of elements, Journal of Optimization Theory and Applications (in print), 2008
Mészáros, Cs.: Detecting ''dense'' columns in linear for interior point methods, Computational Optimization and Applications 36 (2-3) pp. 309-320, 2007
Isac, G. - Németh, S. Z.: Dualaty in multivalued complementarity theory by using inversions and scalar derivatives, Journal of Global Optimization 33 pp. 197-213, 2005
Bergsma, W. P. - Rapcsák, T.: An exact penalty method for smooth equality constrained optimization with application to maximum likelihood estimation, EURANDOM Annual Report, 2005
Bozóki, S. - Rapcsák. T.: On Saaty's and Kockodaj's inconsistencies of pairwise comparison matrices, Journal of Global Optimization (accepted), 2008
Isac, G. - Németh, S. Z.: The asymptotic Browder-Hartman-Stampacchia condition and interior bands of ε-solutions for nonlinear complementarity problems, Rocky Mountain Journal of Mathematics 6 (37) 1917-1940, 2007
Isac, G. - Németh, S. Z.: The nonexistence of a regular expectional family elements. The necessary and sufficient condition. Applications to complementarity, Journal of Global Optimization (accepted), 2008
Mészáros, Cs.: On numerical issues of interior point methods, SIAM Journal of Matrix Analysis (accepted), 2008
Németh, S. Z.: Inequalities characterizing coisotone cones in Euclidean spaces, Positivity 11 (3) pp. 469-475, 2007
Rapcsák, T.: On pseudolinearity of quadratic fractional functions, Optimization Letters 1, pp. 193-200, 2007
Rapcsák, T.: Sectional curvatures in nonlinear optimization, Journal of Global Optimization (in print), 2008
Kéri, G.: On small covering codes in arbitrary mixed Hamming spaces, Studia Scientiarum Mathematicarum Hungarica 44 (4) pp. 517-534, 2007
Rapcsák, T. - Ujvári, M.: Some results on pseudolinear quadratic fractional function, Central European Journal of Operations Research accepted), 2008
Forgó, F. - Fülöp, J.: On the implementation of th L-Nash bargaining in two-person bargaining games, Central European Journal of Operations Reserach (accepted), 2008
Fülöp, J.: A method for approximating pairwise comparison matrices by consistent matrices, Journal of Global Optimization (accepted), 2008
Isac, G. - Németh, S. Z.: Regular exponential family of elements with respect to isotone projection cones in Hilbert spaces and complementarity problems, Optimization Letters (accepted), 2008
Bozóki, S.: Solution of the Least Squares Method problem of pairwise comparison matrices, Central European Journal of Operations Research (accepted), 2008
Kéri, G.: The covering radius of extreme binary 2-surjective codes, Des. Codes Cryptogr. 46 pp. 191-198, 2008



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