9 resultados para preconditioning saddle point problems

em Bulgarian Digital Mathematics Library at IMI-BAS


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AMS subject classification: 65K10, 49M07, 90C25, 90C48.

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An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

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2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05

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2000 Mathematics Subject Classification: 62N02

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∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

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We prove some multiplicity results concerning quasilinear elliptic equations with natural growth conditions. Techniques of nonsmooth critical point theory are employed.

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* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).

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This is a review of methodology for the algorithmic study of some useful models in point process and queueing theory, as discussed in three lectures at the Summer Institute at Sozopol, Bulgaria. We provide references to sources where the extensive details of this work are found. For future investigation, some open problems and new methodological approaches are proposed.

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2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.