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On approximation in multistage stochastic programs: Markov dependence

Vlasta Kaňková, Martin Šmíd (2004)

Kybernetika

A general multistage stochastic programming problem can be introduced as a finite system of parametric (one-stage) optimization problems with an inner type of dependence. Evidently, this type of the problems is rather complicated and, consequently, it can be mostly solved only approximately. The aim of the paper is to suggest some approximation solution schemes. To this end a restriction to the Markov type of dependence is supposed.

On continuous convergence and epi-convergence of random functions. Part I: Theory and relations

Silvia Vogel, Petr Lachout (2003)

Kybernetika

Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic optimization....

On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications

Silvia Vogel, Petr Lachout (2003)

Kybernetika

Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.

On convergence of the empirical mean method for non-identically distributed random vectors

E. Gordienko, J. Ruiz de Chávez, E. Zaitseva (2014)

Applicationes Mathematicae

We consider the following version of the standard problem of empirical estimates in stochastic optimization. We assume that the underlying random vectors are independent and not necessarily identically distributed but that they satisfy a "slow variation" condition in the sense of the definition given in this paper. We show that these assumptions along with the usual restrictions (boundedness and equicontinuity) on a class of functions allow one to use the empirical mean method to obtain a consistent...

On M -stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling

René Henrion, Werner Römisch (2007)

Applications of Mathematics

Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result...

On modelling planning under uncertainty in manufacturing.

A. Alonso-Ayuso, L. F. Escudero, M.T. Ortuño (2007)

SORT

We present a modelling framework for two-stage and multi-stage mixed 0-1 problems under uncertainty for strategic Supply Chain Management, tactical production planning and operations assignment and scheduling. A scenario tree based scheme is used to represent the uncertainty. We present the Deterministic Equivalent Model of the stochastic mixed 0-1 programs with complete recourse that we study. The constraints are modelled by compact and splitting variable representations via scenarios.

On precision of stochastic optimization based on estimates from censored data

Petr Volf (2014)

Kybernetika

In the framework of a stochastic optimization problem, it is assumed that the stochastic characteristics of optimized system are estimated from randomly right-censored data. Such a case is frequently encountered in time-to-event or lifetime studies. The analysis of precision of such a solution is based on corresponding theoretical properties of estimated stochastic characteristics. The main concern is to show consistency of optimal solution even in the random censoring case. Behavior of solutions...

On Solving the Maximum Betweenness Problem Using Genetic Algorithms

Savić, Aleksandar (2009)

Serdica Journal of Computing

In this paper a genetic algorithm (GA) is applied on Maximum Betweennes Problem (MBP). The maximum of the objective function is obtained by finding a permutation which satisfies a maximal number of betweenness constraints. Every permutation considered is genetically coded with an integer representation. Standard operators are used in the GA. Instances in the experimental results are randomly generated. For smaller dimensions, optimal solutions of MBP are obtained by total enumeration. For those...

On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies

Dietmar Ferger (2011)

Kybernetika

Let ϵ - ( Z ) be the collection of all ϵ -optimal solutions for a stochastic process Z with locally bounded trajectories defined on a topological space. For sequences ( Z n ) of such stochastic processes and ( ϵ n ) of nonnegative random variables we give sufficient conditions for the (closed) random sets ϵ n - ( Z n ) to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.

On using multistage linking constraints for stochastic optimization as a decision-making aid

Laureano F. Escudero (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

We present a model1ing framework for multistage planning problems under uncertainty in the objective function coefficients and right-hand-side. A multistagy scenario analysis scheme with partial recourse is used. So, the decisíon polícy can be implemented for a given set of initial time periods (so-called implementable time stage), such that the solution for the other periods lioes not need' to be anticipated and, then, it depends upon the scenario group to occur at each stage. In any ca~e the solution...

Currently displaying 61 – 80 of 118