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Economic and financial processes are mostly simultaneously influenced by a random factor and a decision parameter. While the random factor can be hardly influenced, the decision parameter can be usually determined by a deterministic optimization problem depending on a corresponding probability measure. However, in applications the “underlying” probability measure is often a little different, replaced by empirical one determined on the base of data or even (for numerical reason) replaced by simpler...
We consider a strong NP-hard single-machine scheduling problem with deadlines and minimizing the total weight of late jobs on a single machine (). Processing times are deterministic values or random variables having Erlang distributions. For this problem we study the tolerance to random parameter changes for solutions constructed according to tabu search metaheuristics. We also present a measure (called stability) that allows an evaluation of the algorithm based on its resistance to random parameter...
This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, -optimal solutions are considered. The setup is illustrated on consistency of a --estimator in linear regression model.
* This work was supported by the CNR while the author was visiting the University of Milan.To a convex set in a Banach space we associate a convex function
(the separating function), whose subdifferential provides useful information on the
nature of the supporting and exposed points of the convex set. These points are
shown to be also connected to the solutions of a minimization problem involving the
separating function. We investigate some relevant properties of this function and of
its conjugate...
This work concerns Markov decision processes with finite state space and compact action sets. The decision maker is supposed to have a constant-risk sensitivity coefficient, and a control policy is graded via the risk-sensitive expected total-reward criterion associated with nonnegative one-step rewards. Assuming that the optimal value function is finite, under mild continuity and compactness restrictions the following result is established: If the number of ergodic classes when a stationary policy...
The numerical modeling of the fully developed Poiseuille flow of a newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
The numerical modeling of the fully developed Poiseuille flow
of a Newtonian fluid in a square section with
slip yield boundary condition at the wall is presented.
The stick regions in outer corners and the slip region in the center
of the pipe faces are exhibited.
Numerical computations cover the complete range of the dimensionless number describing
the slip yield effect, from a full slip to a full stick flow regime.
The resolution of variational inequalities
describing the flow is based on the...
We consider the following bottleneck transportation problem with both random and fuzzy factors. There exist supply points with flexible supply quantity and demand points with flexible demand quantity. For each supply-demand point pair, the transportation time is an independent positive random variable according to a normal distribution. Satisfaction degrees about the supply and demand quantity are attached to each supply and each demand point, respectively. They are denoted by membership functions...
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