We analyze the two cut generation scheme in the analytic center cutting plane method. We propose an optimal updating direction when the two cuts are central. The direction is optimal in the sense that it maximizes the product of the new slacks within the trust region defined by Dikin's...

In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only finite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then...

This paper is the second part of our study of Blackwell optimal policies in Markov decision chains with a Borel state space and unbounded rewards. We prove that a stationary policy is Blackwell optimal in the class of all history-dependent policies if it is Blackwell optimal in the class of...

Solutions of portfolio optimization problems are often influenced by errors or misspecifications due to approximation, estimation and incomplete information. Selected methods for analysis of results obtained by solving stochastic programs are presented and their scope illustrated on generic...

In this paper we consider the general question in the field of mathematics of whether some properties or algorithms that hold in finite dimension spaces also hold in function spaces. We answer this question concerning the very well-known Weiszfeld algorithm for the Weber problem. In order to do...

We study coalitional values for games in generalized characteristic function form. There are two extensions of the Shapley value (Shapley (1953)) in this context, one introduced by Nowak and Radzik (1994) and the other introduced by us. We generalize both values to games with a priori unions in...

We consider unconstrained finite minimax problems where the objective function is described as a maximum of functions f <Superscript>k</Superscript>∈C <Superscript>3</Superscript>(ℜ<Superscript>n</Superscript>,ℜ). We propose a parametric embedding for the minimax problem and, assuming that the corresponding parametric optimization problem belongs to the generic class...</superscript></superscript></superscript>

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will...

In [1], we gave a unified variational principle for vector valued functions. In this paper, we give four equivalents of a corollary of this principle, generalizing the equivalence results of [3] to the vector case and improving the equivalence results of [5]. We also applied one of the...

In the paper a discrete time manufacturing system consisting of a machine that produces one kind of goods so as to meet a random demand that is modelized by a finite state ergodic Markov chain is considered. Using a discounted cost approximation an average cost per unit time control problem is...