An exponential example for Terlaky's pivoting rule for the criss-cross simplex method

Recently T. Terlaky has proposed a new pivoting rule for the criss-cross simplex method for linear programming and he proved that his rule is convergent. In this note we show that the required number of iterations may be exponential in the number of variables and constraints of the problem.     

Image space approach to penalty methods

In this paper, we introduce a unified framework for the study of penalty concepts by means of the separation functions in the image space (see Ref. 1). Moreover, we establish new results concerning a correspondence between the solutions of the constrained problem and the limit points of the unconstrained minima. Finally, we analyze some known classes of penalty functions and some known classical results about penalization, and we show that they can be derived from our results directly.     

On differential stability in stochastic programming

In this paper optimal solutions of a stochastic programming problem are considered as functions of the underlying probability distribution. Their directional derivatives, in the sense of Gâteaux, are calculated by applying some recent results from the sensitivity analysis of nonlinear programs. These derivatives are employed as a heuristic device in order to derive the asymptotic distribution of statistical estimators of the optimal solutions.     

Cutting-plane proofs in polynomial space

Following Chvátal, cutting planes may be viewed as a proof system for establishing that a given system of linear inequalities has no integral solution. We show that such proofs may be carried out in polynomial workspace.Research supported by Sonderforschungsbereich 303 (DFG), Institut für Operations Research, Universität Bonn, FR Germany and by NSF grant ECS-8611841.     

Solving multistage asset investment problems by the sample average approximation method

The vast size of real world stochastic programming instances requires sampling to make them practically solvable. In this paper we extend the understanding of how sampling affects the solution quality of multistage stochastic programming problems. We present a new heuristic for determining good feasible solutions for a multistage decision problem. For power and log-utility functions we address the question of how tree structures, number of stages, number of outcomes and number of assets affect the solution quality. We also present a new method for evaluating the quality of first stage decisions.     

Two-stage integer programs with stochastic right-hand sides: a superadditive dual approach

We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to find an optimal tender. We show that our method can solve randomly generated instances whose extensive forms are several orders of magnitude larger than the extensive forms of those instances found in the literature. This work is supported by National Science Foundation grants DMI-0217190 and DMI-0355433.     

Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach

In this paper, we propose a design method of guaranteed cost controllers for uncertain large-scale systems with time delays in subsystem interconnections using delayed feedback. Using the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.Communicated by Q. C. ZhaoThe authors thank the Associate Editor and three anonymous referees for careful reading and useful suggestions.     

On the optimality equation for average cost Markov control processes with Feller transition probabilities

We consider Markov control processes with Borel state space and Feller transition probabilities, satisfying some generalized geometric ergodicity conditions. We provide a new theorem on the existence of a solution to the average cost optimality equation.     

Magnetization relaxation of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics driven by DC/AC magnetic field

The response of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics subjected to alternating current(AC) or direct current(DC) bias magnetic field is evaluated by the reaction–diffusion equation for the probability distribution function of the molecular concentration in the spherical coordinate system. The magnetization function and the probability distribution function of the magnetic particles in the reaction system are derived by using the Legendre polynomials and Laplace transform. We discuss the characteristics of magnetization and probability distribution of the magnetic particles with different anisotropic parameters driven by a DC and AC magnetic fields, respectively. It is shown that both the magnetization and the probability distribution decrease with time increasing due to the reaction process. The uniformity of the probability distribution and the amplitude of the magnetization are both affected by the anisotropic parameters.Meanwhile, the difference between the case with linear reaction dynamics and the non-reaction case is discussed.