Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

The mixed temporal game 1×1 with uncertain actions

100%
Cegielski A.
Mathematica Applicanda
|
1980
|
tom 8
|
nr 16
PL
.
EN
Author's introduction: "The game solved in the present paper belongs to a class of temporal games whose general model was given by S. Karlin [Mathematical methods and theory in games, programming and economics, Addison-Wesley, Reading, Mass., 1959; MR0111634]. The rules are as follows. There are two opposing players, A and B. Each player has a certain number of actions which he can take in the time interval [0,1]. Neither player knows the number of actions he or his opposer has. Each player knows only the distribution of the number of actions for him and his opponent. More precisely, let k1 denote the number of actions of player A and k2 the number of actions of player B, and let k1 and k2 be independent random variables. The distributions of these random variables are as follows: P(k1=1)=p, P(k1=0)=1−p, P(k2=1)=q, P(k2=0)=1−q, p,q∈(0,1]. The opponent knows only both distributions. Thus player A [player B] knows beforehand that he as well as his opponent has zero or one action with the probability given above. If player A has an action then it is silent, i.e., his opponent does not know the moment when the action is taken. If player B has an action it is noisy, i.e. his opponent knows the moment when the action is taken. As a result of the action the player can win or, equivalently, his opponent can lose. A win can be achieved according to the probability given above. If player A [player B] takes an action at time t, then the probability of winning is equal to P(t) [to Q(t)]. Functions P(t) and Q(t) are called payoff functions. These functions satisfy the following conditions: (1) P(t) and Q(t) are differentiable and P′(t)>0 and Q′(t)>0 for t∈(0,1); (2) P(0)=Q(0)=0, P(1)=Q(1)=1. Both functions are known to the players before the game begins. The game ends when one player wins or when neither wins at time t=1. If only player A wins he obtains the payoff +1 from his opponent, and likewise if only B wins he obtains the payoff +1. In the remaining cases the payoff is equal to zero. Y. Teraoka solved a temporal game 1×1 with uncertain actions [Rep. Himeji Inst. Tech. 28 (1975), 1–8; RŽMat 1976:8 V662]. If in the game, played according to the rules given above, we put p=q=1, then this type of game is a particular case of the game solved by A. Styszyński [Zastos. Mat. 14 (1974), 205–225; MR0351487]. Here we present a solution to a more generalized game in which the first player has n actions. The game defined above can be interpreted as a duel. In the course of an action shots are fired and a win is achieved when the opponent is hit. The payoff function is then called an accuracy function. The duelists do not know beforehand whether the weapons are loaded or accurate. They know only the probability of drawing a loaded weapon. We shall use this interpretation in later sections of the paper. This game can also be viewed as an advertising war. Two enterprises are engaged in an advertising war to win a contract. Here an action can be viewed as setting in motion the advertising machine of the player's company. A win is achieved when the contract is awarded to the player's company as a result of his action. Before the campaign the players do not know whether they will receive funds from their central offices to engage in the advertising war."
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Properties of projection and penalty methods for discretized elliptic control problems

63%
Cegielski A., Grossmann C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2007
|
tom 27
|
nr 1
23-41
EN
In this paper, properties of projection and penalty methods are studied in connection with control problems and their discretizations. In particular, the convergence of an interior-exterior penalty method applied to simple state constraints as well as the contraction behavior of projection mappings are analyzed. In this study, the focus is on the application of these methods to discretized control problem.
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Selection strategies in projection methods for convex minimization problems

63%
Cegielski A., Dylewski R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 1
97-123
EN
We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical results show that the presented selection strategies ensure long steps and lead to an essential acceleration of the convergence of projection methods.
4
Content available remote

A generalization of the Opial's theorem

32%
Cegielski A.
Control and Cybernetics
|
2007
|
tom 36
|
nr 3
601-610
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.