Michael Stieglitz

On polychotomous search problems

Abstract The paper gives a unified treatment of those stochastic sequential search problems where in each state the searcher may decompose according to a given scheme the current search region in a finite number of parts upon which one obtains the error-free information in which of the parts the object is hidden. Many examples are given to show the generality of the model. The main results are: (a) a rigorous proof of the dynamic programming approach, (b) the reduction of the state space for problems with translation invariant data, (c) a dynamic programming proof for the computationally very attractive property of monotonicity and Lipschitz continuity of optimal search rules for two important special models, one of which has been investigated by Hassin (1984) using methods from information theory.

Increasing and Lipschitz continuous minimizers in one-dimensional linear-convex systems without constraints: The continuous and the discrete case

We consider a stochastic control model with linear transition law and arbitrary convex cost functions, a far-reaching generalization of the familiar linear quadratic model. Firstly conditions are given under which the continuous state version has minimizersfn at each stagen which are increasing and in addition either right continuous or continuous or Lipschitz continuous with explicitly given Lipschitz constant. For the computationally important discrete version we verify some analogous properties under stronger assumptions.

Beste Quadraturformeln für Integrale mit einer Gewichtsfunktion

AbstractLet

Absorbing Dynamic Programs and Acyclic Networks

E = (e_{\mu v} )_{\mu = 0,v = 0}^{m,n - 1}

Bayesian Control Models

be a fixed matrix with elements that are 0 or 1 and letX be a fixed set ofm+1 different knots. The problem is to find necessary and sufficient conditions for (E, X) to guarantee the existence of a quadrature formula with a remainder term of type

Markovian Decision Processes with Large and with Infinite Horizon

R(f): = \int\limits_0^1 {w(t)f(t)dt---\sum\limits_{e_{\mu v} = 1} {a_{\mu v} } f(v)(x_\mu )}