2,682 research outputs found
Nemlineáris egyensúlyi rendszerek elméleti és módszertani kérdései = Theoretical and methodological issues of nonlinear equilibrium systems
A nemlineáris egyensĂşlyi rendszerek terĂĽletĂ©n Ăşj eredmĂ©nyeket Ă©rtĂĽnk el egyes feladatosztályok megoldhatĂłságának skaláris deriváltakra alapozott jellemzĂ©sĂ©vel. A nemlineáris egyensĂşlyi rendszerek egy Ăşj megközelĂtĂ©sĂ©t adtuk az izotĂłn projekciĂłs kĂşpok Ă©s kiterjesztĂ©seik segĂtsĂ©gĂ©vel, Ă©s Ăşj eredmĂ©nyeket mutattunk be izoton projekciĂłs kĂşpokkal törtĂ©nĹ‘ rekurziĂłk konvergenciáját illetĹ‘en. Megmutattuk a metszetgörbĂĽlek nemlineáris optimalizálásban betöltött szerepĂ©t, Ă©s kvadratikus törtfĂĽggvĂ©nyek speciális tulajdonságaival is foglalkoztunk. Fontos mĂłdszertani Ă©s implementáciĂłs eredmĂ©nyeket Ă©rtĂĽnk el a kvadratikus optimalizálás belsĹ‘ pontos mĂłdszereinek terĂĽletĂ©n is. Ăšj blokkolási sĂ©mát fejlesztettĂĽnk ki a belsĹ‘ pontos algoritmusoknál elĹ‘fordulĂł szimmetrikus mátrixok faktorizáciĂłjához. A kvadratikus feltĂ©telek melletti konvex optimalizálás fontos feladatosztály a folytonos optimalizálásban. Megmutattuk, hogy belsĹ‘ pontos mĂłdszerekkel ez a feladatosztály nagy mĂ©retekben is hatĂ©konyan kezelhetĹ‘. Sikeresen alkalmaztuk a nemlineáris programozást döntĂ©si feladatok megoldásánál, elsĹ‘sorban páros összhasonlĂtási mátrixok konzisztens márixokkal valĂł közelĂtĂ©sĂ©vel kapcsolatban. Ăšj mĂłdszereket mutattunk be a legkisebb nĂ©gyzetek cĂ©lfĂĽggvĂ©nyű közelĂtĂ©s globális optimális megoldásainak meghatározására, valamint kiterjesztettĂĽk a sajátvektor mĂłdszert a nem teljesen kitöltött páros összehasonlĂtási mátrixok esetĂ©re | New results have been achieved in the field of nonlinear equilibrium problems by characterizing the solvability of some problem classes based on scalar derivatives. A new approach has been presented for the nonlinear equilibrium systems by the help of isotone projection cones and their extensions. Also, new results were presented on the convergence of recursions with isotone projection cones. We pointed out the role of sectional curvatures in nonlinear optimization. Some special properties of quadratic fractional functions have been also dealt with. We achieved important methodological and implementational results in the field of interior point methods of quadratic optimization. A new blocking scheme was developed for the symmetric matrix factorizations arising in interior point methods. An important class of the continuous optimization is that of the quadratically constrained convex problems. New techniques have been presented that improve the efficiency of interior point methods when solving quadratically constrained large-scale problems. Nonlinear programming was applied successfully at solving some decision problems, mainly at approximating pairwise comparison matrices by consistent ones. We presented new methods for finding the global optimal solutions in the case of approximating in the least squares sense. We also extended the eigenvector method for the case of incomplete pairwise comparison matrices
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
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